$\frac{1}{\cos ^{2} \theta}-\frac{1}{\cot ^{2} \theta} = \dots$

The value of the expression $\left[\frac{\sin ^{2} 22^{\circ}+\sin ^{2} 68^{\circ}}{\cos ^{2} 22^{\circ}+\cos ^{2} 68^{\circ}}+\sin ^{2} 63^{\circ}+\cos 63^{\circ} \sin 27^{\circ}\right]$ is:

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

If $1+\sin ^{2} \theta=3 \sin \theta \cos \theta,$ then prove that $\tan \theta=1$ or $\frac{1}{2}$.

If $2 \sin^{2} \theta - \cos^{2} \theta = 2$,then find the value of $\theta$. (in $^{\circ}$)

If $\operatorname{cosec} A = \sqrt{10}$,then $\sin A = \dots$