Answers
We know that,
[tex]\dag\bf\:sin^2A=\dfrac{1-cos2A}{2}[/tex]
[tex]\dag\bf\:sin2A=2sinA\:cosA[/tex]
___________________________________
Now, Let's solve !
[tex]\leadsto\:\bf\dfrac{sin^2A-sin^2B}{sinA\:cosA-sinB\:cosB}[/tex]
[tex]\leadsto\:\sf\dfrac{\frac{1-cos2A}{2}-\frac{1-cos2B}{2}}{\frac{2sinA\:cosA}{2}-\frac{2sinB\:cosB}{2}}[/tex]
[tex]\leadsto\:\sf\dfrac{1-cos2A-1+cos2B}{sin2A-sin2B}[/tex]
[tex]\leadsto\:\sf\dfrac{2sin\frac{2A+2B}{2}\:sin\frac{2A-2B}{2}}{2sin\frac{2A-2B}{2}\:cos\frac{2A+2B}{2}}[/tex]
[tex]\leadsto\:\sf\dfrac{sin(A+B)}{cos(A+B)}[/tex]
[tex]\leadsto\:\bf{tan(A+B)}[/tex]
Answer: see proof below
Step-by-step explanation:
Use the Power Reducing Identity: sin² Ф = (1 - cos 2Ф)/2
Use the Double Angle Identity: sin 2Ф = 2 sin Ф · cos Ф
Use the following Sum to Product Identities:
[tex]\sin x - \sin y = 2\cos \bigg(\dfrac{x+y}{2}\bigg)\sin \bigg(\dfrac{x-y}{2}\bigg)\\\\\\\cos x - \cos y = -2\sin \bigg(\dfrac{x+y}{2}\bigg)\sin \bigg(\dfrac{x-y}{2}\bigg)[/tex]
Proof LHS → RHS
[tex]\text{LHS:}\qquad \qquad \qquad \dfrac{\sin^2A-\sin^2B}{\sin A\cos A-\sin B \cos B}[/tex]
[tex]\text{Power Reducing:}\qquad \dfrac{\bigg(\dfrac{1-\cos 2A}{2}\bigg)-\bigg(\dfrac{1-\cos 2B}{2}\bigg)}{\sin A \cos A-\sin B\cos B}[/tex]
[tex]\text{Half-Angle:}\qquad \qquad \dfrac{\bigg(\dfrac{1-\cos 2A}{2}\bigg)-\bigg(\dfrac{1-\cos 2B}{2}\bigg)}{\dfrac{1}{2}\bigg(\sin 2A-\sin 2B\bigg)}[/tex]
[tex]\text{Simplify:}\qquad \qquad \dfrac{1-\cos 2A-1+\cos 2B}{\sin 2A-\sin 2B}\\\\\\.\qquad \qquad \qquad =\dfrac{-\cos 2A+\cos 2B}{\sin 2A - \sin 2B}\\\\\\.\qquad \qquad \qquad =\dfrac{\cos 2B-\cos 2A}{\sin 2A-\sin 2B}[/tex]
[tex]\text{Sum to Product:}\qquad \qquad \dfrac{-2\sin \bigg(\dfrac{2B+2A}{2}\bigg)\sin \bigg(\dfrac{2B-2A}{2}\bigg)}{2\cos \bigg(\dfrac{2A+2B}{2}\bigg)\sin \bigg(\dfrac{2A-2B}{2}\bigg)}[/tex]
[tex]\text{Simplify:}\qquad \qquad \dfrac{-2\sin (A + B)\cdot \sin (-[A - B])}{2\cos (A + B) \cdot \sin (A - B)}[/tex]
[tex]\text{Co-function:}\qquad \qquad \dfrac{2\sin (A + B)\cdot \sin (A - B)}{2\cos (A + B) \cdot \sin (A - B)}[/tex]
[tex]\text{Simplify:}\qquad \qquad \quad \dfrac{\cos (A+B)}{\sin (A+B)}\\\\\\.\qquad \qquad \qquad \quad =\tan (A+B)[/tex]
LHS = RHS: tan (A + B) = tan (A + B) [tex]\checkmark[/tex]
Related Questions
Simplify: -3(y+2)^2-5+6y
Answers
Answer:3y^2+18y+7
:) happy to help
What is the value of 6 x 90.6 ?
Answers
Answer:
543.6
Step-by-step explanation:
=> 6 x 90.6
=> 543.6
Si la época prehistórica sucedió desde hace 2.5 millones de años a.C., hasta hace 2.500 años a.C.; el período Paleolítico (2.5 millones de años a.C. Hasta 10.000 a.C.; el Mesolítico 10.000 a.C. Hasta 5.000 a.C. Y, el Neolítico sucedió desde el 5.000 a.C. Hasta el 2.500 a.C. ¿A qué fracción de la época prehistórica corresponde el período paleolítico? *
Answers
Answer:
El período paleolítico corresponde a [tex]\frac{332}{333}[/tex] de la época prehistórica.
Step-by-step explanation:
En primer lugar, se determina la extensión de tiempo, medida en años, tanto de la época prehistórica como el período paleolítico: (Nótese que el signo negativo significa a.C.)
Época Prehistórica
[tex]\Delta T = -2500-(-2500000)[/tex]
[tex]\Delta T = 2497500\,years[/tex]
Período Paleolítico
[tex]\Delta t = -10000 - (-2500000)[/tex]
[tex]\Delta t = 2490000\,years[/tex]
La fracción de la época prehistórica que corresponde al período paleolítico es:
[tex]r = \frac{\Delta t}{\Delta T}[/tex]
[tex]r = \frac{2490000\,years}{2497500\,years}[/tex]
[tex]r = \frac{332}{333}[/tex]
El período paleolítico corresponde a [tex]\frac{332}{333}[/tex] de la época prehistórica.
The ratio of the number of baskets made by to Tony to the number of baskets made by Colin is 2 to 3. Tony made 10 baskets.How many baskets did Colin make?
Answers
Answer:
I believe the answer would be 15
Step-by-step explanation:
This is because the ratio is 2 to 3 and you would divide it in half so you get one part then times it by three to get the second part of the ratio.
So it would be 10/2=5 then 5 times 3 to get 15. Therefore, 10 to 15
Answer:
15 baskets
Step-by-step explanation:
Step 1 : write a statement
Tony : Colin
2 : 3
10 : ?
Step 2: Cross multiply
i.e. 10×3=30
30÷2=15
Using inductive reasoning, what number is the most reasonable conjecture for the next number in the pattern 27,23,19,15,
Answers
Answer:
11
Step-by-step explanation:
The pattern here is to subtract by 4, so 15-4=11
A 12.5 oz box of cereal has a price of $2.07. What is the unit ratio of price to weight rounded to the nearest cent?
Answers
Answer:
16 cents
Step-by-step explanation:
The answer is 16 cents because 207 cents divided by 12.5 oz equals 16 cents.
The table shows the height of the tree that Margo planted over an 11-month period.
A 2-column table with 6 rows titled Growth of Margo's Tree. The first column is labeled Month with entries 1, 3, 5, 7, 9, 11. The second column is labeled Height of Tree (feet) with entries 1.4, 1.5, 2.1, 2.7, 3.0, 1.8.
Which statement can be supported by the information in the table?
The tree increased in height each month during the entire 11-month period.
The tree decreased in height each month during the entire 11-month period.
The tree increased in height each month until the time period between month 9 and month 11.
The tree decreased in height each month until the time period between month 9 and month 11.
Answers
Answer:
The answer is c
Step-by-step explanation:
just did it on edg
Answer:
The answer is: C
Solve for d. dt=v What is d equal to? A. d=vt B. d=t/v C. d=v-t D. d=v/t
Answers
Answer: I think the answer is "d = vt"
Step-by-step explanation:
Multiply both sides of the equation by;
t * d = v * (t)
Multiply, v by t
Answer; d = vt
Hope this helps :)
The value of d, is equivalent to d = v/t.
What is a function?
An expression in mathematics defines a relationship between one variable (the independent variable, x) and another variable (the dependent variable, y). For example -
f(x) = 4x + 6
Given is the following equation -
dt = v
We have -
dt = v
d = v/t
Therefore, the value of d, is equivalent to d = v/t.
To solve more questions on functions, visit the link below -
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Find the straight pay:$9.25 per hour x 35 hours.
Answers
Answer:
323.75 hours is the answer
Which represents a function
Answers
Answer:
the one on the right
Step-by-step explanation:
one input cannot have more than one output
Please help, Solve Systems of Linear Equations
Answers
Answer:
x = 1 , y = 1 , z = -3
Step-by-step explanation using elimination:
Solve the following system:
{3 x + 2 y - z = 8 | (equation 1)
2 z + 2 x = -4 | (equation 2)
3 y + x = 4 | (equation 3)
Subtract 2/3 × (equation 1) from equation 2:
{3 x + 2 y - z = 8 | (equation 1)
0 x - (4 y)/3 + (8 z)/3 = -28/3 | (equation 2)
x + 3 y+0 z = 4 | (equation 3)
Multiply equation 2 by 3/4:
{3 x + 2 y - z = 8 | (equation 1)
0 x - y + 2 z = -7 | (equation 2)
x + 3 y+0 z = 4 | (equation 3)
Subtract 1/3 × (equation 1) from equation 3:
{3 x + 2 y - z = 8 | (equation 1)
0 x - y + 2 z = -7 | (equation 2)
0 x+(7 y)/3 + z/3 = 4/3 | (equation 3)
Multiply equation 3 by 3:
{3 x + 2 y - z = 8 | (equation 1)
0 x - y + 2 z = -7 | (equation 2)
0 x+7 y + z = 4 | (equation 3)
Swap equation 2 with equation 3:
{3 x + 2 y - z = 8 | (equation 1)
0 x+7 y + z = 4 | (equation 2)
0 x - y + 2 z = -7 | (equation 3)
Add 1/7 × (equation 2) to equation 3:
{3 x + 2 y - z = 8 | (equation 1)
0 x+7 y + z = 4 | (equation 2)
0 x+0 y+(15 z)/7 = -45/7 | (equation 3)
Multiply equation 3 by 7/15:
{3 x + 2 y - z = 8 | (equation 1)
0 x+7 y + z = 4 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Subtract equation 3 from equation 2:
{3 x + 2 y - z = 8 | (equation 1)
0 x+7 y+0 z = 7 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Divide equation 2 by 7:
{3 x + 2 y - z = 8 | (equation 1)
0 x+y+0 z = 1 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Subtract 2 × (equation 2) from equation 1:
{3 x + 0 y - z = 6 | (equation 1)
0 x+y+0 z = 1 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Add equation 3 to equation 1:
{3 x+0 y+0 z = 3 | (equation 1)
0 x+y+0 z = 1 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Divide equation 1 by 3:
{x+0 y+0 z = 1 | (equation 1)
0 x+y+0 z = 1 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Collect results:
Answer: {x = 1 , y = 1 , z = -3
Owen is fishing from a dock he starts with the bait 2 feet below the surface he reels out the boat 19 feet then reels it back in 7 feet what is the final position of the bait relative to the surface of the water
Answers
Answer:
The bait is 14 feet below the water surface
Step-by-step explanation:
Here, we want to know the final position of the bait relative to the surface of the water.
Firstly, he starts with the bait at 2 feet below the water surface. The reels out the bait a further 19 feet, the new position of the bait relative to the water surface will be 2 + 19 = 21 feet
Now, he reels the bait back by 7 feet.
Thus, the new depth of the bait relative to the water surface will be 21-7 = 14 feet
Twelve more than a number is the product of -3 and 6. Translate using n
Answers
Answer: n + 12 = -18 or n + 12= -3(6)
Step-by-step explanation:
12 more than a number means 12 is added to the number so the expression will be n + 12 and the product of -3 and 6 is the same as -3 times 6 which is -18 . n + 12 has to equal -18 .
n + 12 = -18 now subtract 12 from both sides
-12 -12
n= -30
So the number is -30
I NEED SERIOUS HELP NOW PLZ
The expression (y – 9)2 is equivalent to which expression. Simplify and write in standard form. Show your work.
Answers
Answer:
Step-by-step explanation:
Hello,
[tex](y-9)^2=(y-9)(y-9)=y^2-2*9*y+9^2=y^2-18y+81[/tex]
thanks
Answer:
yes
Step-by-step explanation:
Figures in square brackets are estimated standard errors of the coefficient estimates. What is the value of the test statistic for the hypothesis that the coefficient of is zero against the alternative that is less than zero?
Answers
Henry needs 2 pints of red paint and 3 pints of yellow paint to get a specific shade orange. If he uses 9 pints of yellow paint and wants the same orange color, how many pints of paint will he need altogether. Explain how you know
Answers
Answer:
15 pints of paint 6 red 9 yellow
Step-by-step explanation:
3x3=9 so 9 yellow pints
and 2x3=6 so 6 red pints
6+9=15 so 15 pints of paint in total
A rectangle has height to width ratio 3:45. give two examples of dimensions for rectangles that could be scaled version of this rectangle
Answers
Answer:
fr7diyktgjhv fdxgkhgfdxghnjkngfcc
Step-by-step explanation:
rd6klfutgkhjkhfdeswdfgkjhuyt6rdefgthjkiluhgf
Answer:
Step-by-step explanation:
Lucy is going to walk in a fundraising event to raise money for her school band. Her mother has agreed to donate $7.50 to the school for each mile that Lucy walks, plus an additional $25. If Lucy wants to make at least $85.00 from her mother’s donation, how far will she have to walk? Show your work.
Answers
Answer:
8 miles
Step-by-step explanation:
let x= miles she walks
7.50x+25=85
subtract 25 from both
7.50x=60
divide both by 7.50
x=8
is 4 √ 7 2 written in simplest radical form
yes or no
Answers
Answer:
No.
Step-by-step explanation:
Notice that 72 can be written as 8 * 9.
4√72 = 4(√8)(√9) = 4(√8)(3) = 12√8.
Hence the answer is No.
Answer:
no 8[tex]\sqrt{7}[/tex] would be simplified
Step-by-step explanation:
What is the unit rate if a student reads 81 pages in 3 hours?
Answers
Answer:
27 pages per hour
Step-by-step explanation:
81 pages divide by 3 hours. think of it as a fraction and divided 3 on both bottom and top then it gives you 27pages per hour as a fraction
А
B
1. Village A, B and C lie on the edge of the Namib Desert.
Village A is 30 km due North of Village C. Village C is 65 km
due East of A.
Calculate the shortest distance between village C and B,
giving your answer to the nearest 0.1km
Answers
The ratio of yellow to blue skittles in a bag 5:9 if there are 12 more blue skittles in the bag than yellow skittles how many yellow skittles are in the bag
Answers
Answer: 15
Step-by-step explanation: 5/9=15/27. 27-15=12
The number of yellow skittles in the bag are 15 skittles while the number of blue skittles in the bag are 27 skittles.
What is Ratio?A ratio is an ordered pair of numbers x and y which can be written as x / y where y does not equal 0. A proportion is an equation in which two ratios are set equal to each other.
For given information,
The ratio of yellow to blue skittles in the bag is 5:9
The number of blue skittles in the bag = 12 + The number of yellow skittles in the bag= 12+Y
Fraction of the total skittles that are yellow = 5/(5 + 9) = 5/14
Fraction of the total skittles that are blue = 9/(5+9)= 9/14
The total number of skittles = Yellow + Blue
in this Y as yellow; Y+12 as blue.
Y + Y + 12 = 2·Y + 12
The fraction of the total skittles that are blue = 9/14
we have 9/14 × (2·Y + 12) = Y + 12
-> 9 × (2·Y + 12) = 14 × (Y + 12)
-> 18·Y + 108 = 14·Y + 168
-> 18·Y - 14·Y = 168 - 108 = 60
-> 4·Y = 60
-> Y = 60/4 = 15
∴ The number of yellow skittles in the bag = 15
The number of blue skittles is given as = Y + 12 = 15 + 12 = 27.
Thus, the number of yellow skittles in the bag are 15 skittles while the number of blue skittles in the bag are 27 skittles.
Learn more about Ratio, here:
https://brainly.com/question/13419413
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Danny is trying to determine the product between a rational and irrational number
Answers
Answer:
2√3=2√3, which is irrational
How do you divide 506 in the ratio 2:4:5 ?
Answers
Answer:
Step-by-step explanation:
If the ratio is 2:4:5 there are 2+4+5=11 equal parts...
506/11=46
So each part is equal to 46 so 506 in a ratio of 2:4:5 is:
92:184:230
1) f(x) = 3x - 4
g(x) – x2 + 3x
Find f(g(x))
Answers
Answer:
x=4/3
Step-by-step explanation:
Jesse loves to go hiking on rustic trails through trees and along rivers. One day in 20 minutes of hiking she hiked 1 mile. If Jesse hike at a constant rate what would the rate be
Answers
Answer:
0.05 mile per minutes
Step-by-step explanation:
Jesse's rate of hiking (miles per minute) = Total miles covered / Time covered
Miles covered = 1 mile
Time covered = 20 minutes
Jesse's rate of hiking (miles per minute) = Total miles covered / Time covered(minutes)
= 1 mile / 20 minutes
= 0.05 mile per minutes
20 minutes
= 20 × 60 seconds
= 1200 seconds
Jesse's rate of hiking (miles per seconds) = Total miles covered / Total time taken (seconds)
= 1 mile / 1200 seconds
= 0.0008333333333 miles per seconds
Approximately 0.000833 miles per seconds
You spend $300 to start and costs $20 for each dog house
# of dog houses
1
2.
3
4
5
6
7
Total cost to build
Answers
Answer:
15
Step-by-step explanation:because because 300 divided by 20 equals 15 hope this helps
How much should Jenna save up to prepare for car repairs and maintenance? (A lump sum emergency fund just for car repair/maintenance that may come up in the future)
Answers
Answer:
$500 per year.
Step-by-step explanation:
Car repairs and maintenance expense is based on the usage of car as well as its present condition. If the car is bought from showroom and is new then it will incur only small amount of expense as its maintenance but if the car is used by various owners then it is likely that maintenance expense can be huge. The average car repair expense is $500 to $800 per year depending on car condition. Since Jenna car is new she should keep the repair estimate to be minimum that is nearly $500 per year or $42 per month.
Number of girls: 14 Number of boys: 12 Number of students in the class: 26 What is the ratio in simplest form of the number of boys to the number of students in this math class?
Answers
divide by 2 and you get
6 : 13
this can’t be divided anymore so the ratio in simplest form is 6:13
Answer:
6:13
Step-by-step explanation:
I need to know about the gradient
Answers
Answer:
Step-by-step explanation: