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Chapter 7: Q. 61 (page 486)

In Problems 47鈥�72, establish each identity.

cos伪+尾cos伪cos尾=1-tan伪tan尾

Short Answer

Expert verified

The given identity is established.

Step by step solution

01

Step 1. Given Information 

The given expression iscos伪+尾cos伪cos尾=1-tan伪tan尾.

We have to establish each identity.

02

Step 2. Establishing the identity 

We can establish the given expression as an identity by simplifying one side to give the other side.

So, use the sum identity for the cos function,cos伪+尾=cos伪cos尾-sin伪sin尾

L.H.S

cos伪+尾cos伪cos尾=cos伪cos尾-sin伪sin尾cos伪cos尾=1-tan伪tan尾

Thus, L.H.S = R.H.S and the given expression is an identity.

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