SOLUTION: Product to Sum/Sum to Product (TRIGONOMETRY) 1. Express cos38 + cos106 as a PRODUCT. 2. Express cos234 cos125 as SUM (Show full solution) Thank You! :)

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Question 1189940: Product to Sum/Sum to Product (TRIGONOMETRY)
1. Express cos38 + cos106 as a PRODUCT.
2. Express cos234 cos125 as SUM
(Show full solution)
Thank You! :)
Found 2 solutions by math_tutor2020, MathLover1:
Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!

Problem 1

We can use this identity

In this case, A = 38 and B = 106

Recall that cos(-x) = cos(x).

Answer:

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Problem 2

We'll use that previous identity, but in reverse.

We have
(A+B)/2 = 234
(A-B)/2 = 125
as the two arguments in the cosines being multiplied.

For each equation, multiply both sides by 2
A+B = 468
A-B = 250

Then add straight down
2A+0B = 718
2A = 718
A = 718/2
A = 359

This leads to:
A+B = 468
359+B = 468
B = 468-359
B = 109

Therefore,

Answer:

Answer by MathLover1(20850) (Show Source):
You can put this solution on YOUR website!

1. Express as a PRODUCT.
use Sum-to-Product Identity:

2. Express as SUM

use Product-to-Sum Identity: