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Chapter 7: Q. 26 (page 485)

In problem 23-32,find the exact value of the each expression

cos40掳cos10掳+sin40掳sin10掳

Short Answer

Expert verified

The exact value ofcos40掳cos10掳+sin40掳sin10掳=32

Step by step solution

01

Step 1.Given information

The given expressioncos40掳cos10掳+sin40掳sin10掳

02

Step 2.Finding exact value of the given expression

We will use the formula cos(伪-尾)=cos伪cos尾+sin伪sin尾

The indicated expression cos40掳cos10掳+sin40掳sin10掳is in the form of the right side of the formulacos(伪-尾)=cos伪cos尾+sin伪sin尾

where 伪=40掳and尾=10掳

Therefore we get

cos40掳cos10掳+sin40掳sin10掳=cos(40掳-10掳)=cos30掳=32

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