Write 'True' or 'False' and justify your answer.

$\sqrt{\left(1-\cos ^{2} \theta\right) \sec ^{2} \theta}=\tan \theta$

If $\sin A =\frac{1}{2},$ then the value of $\cot A$ is

Prove that,

$(\sin \alpha+\cos \alpha)(\tan \alpha+\cot \alpha)=\sec \alpha+\operatorname{cosec} \alpha$

$\sin ^{2} 1+\sin ^{2} 3+\sin ^{2} 87+\sin ^{2} 89=\ldots \ldots \ldots \ldots$

$8 \sin ^{2} 45-2 \tan ^{2} 60+3 \cot ^{2} 30-2 \cos ^{2} 45$