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Chapter 7: Q. 10 (page 485)

True or FalseIff(x)=sinx andg(x)=cosx then g(伪+尾)=g(伪)g(尾)-f(伪)f(尾).

Short Answer

Expert verified

If f(x)=sinxand g(x)=cosxthen localid="1646462766502" g(伪+尾)=g(伪)g(尾)-f(伪)f(尾).

This is true.

Step by step solution

01

Step 1. Given information 

Given that:

f(x)=sinxg(x)=cosxtheng(伪+尾)=g(伪)g(尾)-f(伪)f(尾).

We have to tell whether this is true or false.

02

Step 2. Apply the sum of the cosine function

Consider the LHS.

g(伪+尾)=cos(伪+尾)=cos伪cos尾-sin伪sin尾

Consider RHS.

g(伪)g(尾)-f(伪)f(尾)=cos伪cos尾-sin伪sin尾

Therefore, L.H.S.=R.H.S.

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