Chapter 14.2, Problem 17PPS

To determine

To Prove :The value of $\cos \theta \cos (-\theta )-\sin \theta \sin (-\theta )=1$

Explanation of Solution

Given information :

We know that, the given equation is $LHS=\cos \theta \cos (-\theta )-\sin \theta \sin (-\theta )$

Proof :

  $\begin{array}{l}\cos (-\theta )=\cos \theta and\sin (-\theta )=-\sin \theta \\ \Rightarrow LHS=\cos \theta \cos \theta -\sin \theta (-\sin \theta )\\ ={\cos }^2\theta -(-{\sin }^2\theta )\\ ={\cos }^2\theta +{\sin }^2\theta \\ =1\\ =RHS\end{array}$