You are given that cos(A)=−5/13, with A in Quadrant II, and sin(B)=7/25, with B in Quadrant II. Find cos(A+B). Give your answer

Question

2 years ago

10

as a fraction.

1 answer:

blsea [12.9K] · Answer 1 · 2023-09-13T09:54:51+03:00

The value of cos(A+B) is 36/325.

<h3>What is Trigonometry?</h3>

The branch of mathematics concerned with specific functions of angles and their application to calculations.

Given:

cos(A)=−5/13

sin(B)=7/25

Now Using identity,

sin²A + cos² A= 1

sin A= √1 - cos² A

sin A = √1- 25/169

sin A= √144/169

sin A= 12/13

Again,

sin²B + cos² B= 1

cos B= √1 - sin² B

cos B = √1- 49/625

cos B= √576/625

cos B= -24/25

Now,

cos (A +B) = cos A cos B - sin A sin B.

= -5/13* (-24/25) - 12/13* 7/25

= 120/325 - 84/325

= 36/325

Hence, the value of cos (A + B) is 36/325.

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