Prove the following trigonometric identities.

We know that, $\sin ^{2} \theta+\cos ^{2} \theta=1$.

So,

$\tan ^{2} \theta \cos ^{2} \theta=(\tan \theta \times \cos \theta)^{2}$

$=\left(\frac{\sin \theta}{\cos \theta} \times \cos \theta\right)^{2}$

$=(\sin \theta)^{2}$

$=\sin ^{2} \theta$

$=1-\cos ^{2} \theta$