Chapter 13.3, Problem 3BGP

To determine

To verify: The given equation is an identity.

Explanation of Solution

Given information: Given equation is $\cos (90°+\theta )=-\sin \theta$ .

Verification:

  $\cos (90°+\theta )=-\sin \theta$

Using sum and difference identity,

  $\begin{array}{l}\cos 90°\cos \theta -\sin 90°\sin \theta =-\sin \theta \\ \Rightarrow 0(\cos \theta )-1(\sin \theta )=-\sin \theta \\ \Rightarrow -\sin \theta =-\sin \theta \end{array}$

Thus, the given equation is an identity.

Hence proved.