When will the values of $\sin \theta$ and $\cos \theta$ be equal?

If $0^{\circ }\le \theta \le {90}^{\circ }$. For what values of $\theta$ does $\sin \theta >\cos \theta$?

Prove the following trigonometric identities: 

$\left(1+\cot \theta -\mathrm{cosec}\theta \right)\left(1+\tan \theta +\sec \theta \right)=2$

Prove that ${\sec }^6\theta ={\tan }^6\theta +3{\tan }^2\theta {\sec }^2\theta +1$

Prove that ${\mathrm{cosec}}^6\theta ={\cot }^6\theta +3{\cot }^2\theta {\mathrm{cosec}}^2\theta +1$

Prove that ${\sin }^{2}A{\cos }^{2}B-{\cos }^{2}A{\sin }^{2}B={\sin }^{2}A-{\sin }^{2}B$