Question

How do you simplify $\left(1+\cos x\right)\left(1-\cos x\right)$?

Answer 1

Simplify the given expression:

The given expression is

$\left(1+\cos x\right)\left(1-\cos x\right)=1-{\cos }^{2}x$ $...\left[\because a^2-b^2=\left(a+b\right)\left(a-b\right)\right]$

We know the identity,

${\sin }^{2}x+{\cos }^{2}x=1$

$\Rightarrow$ ${\sin }^{2}x=1-{\cos }^{2}x$

Hence, $\left(1+cosx\right)\left(1-cosx\right)$ can be simplified into $\mathit{s}\mathit{i}{\mathit{n}}^{\mathbf{2}}\mathit{\theta }$.