State whether the following is true or false. Justify your answer.
The value of $\cos \theta$ increases as $\theta$ increases.

State whether the following is true or false. Justify your answer.
$\sin \theta = \cos \theta$ for all values of $\theta$.

Prove the following identities,where the angles involved are acute angles for which the expressions are defined:
$\left(\frac{1+\tan ^{2} A}{1+\cot ^{2} A}\right)=\left(\frac{1-\tan A}{1-\cot A}\right)^{2}=\tan ^{2} A$

Evaluate:
$\frac{\tan 26^{\circ}}{\cot 64^{\circ}}$

Evaluate the following:
$\frac{5 \cos ^{2} 60^{\circ}+4 \sec ^{2} 30^{\circ}-\tan ^{2} 45^{\circ}}{\sin ^{2} 30^{\circ}+\cos ^{2} 30^{\circ}}$ (in $/12$)

If $A, B$ and $C$ are interior angles of a triangle $ABC$,then show that $\sin \left(\frac{B+C}{2}\right) = \cos \frac{A}{2}$.