Question

How is $\cos (-x)=\cos x$?

Answer 1

Prove the given identity:

The given expression is, $LHS=\cos \left(-x\right)$

$\therefore \cos \left(-x\right)=\sin \left\{90-\left(-x\right)\right\}$ $...\left[\because cosx=sin\left(90°-x\right)\right]$

$=\sin \left(90°+x\right)$

$=\sin 90°\cos x+\cos 90°\sin x$ $...\left[\because sin\left(a+b\right)=sinacosb+cosasinb\right]$

$=\cos x+0$ $...\left[\because sin90°=1;cos90°=0°\right]$

$=\cos x$

$=RHS$

Hence, the given relation $\cos (-x)=\cos x$ has been proved.