If $3 \cot \theta = 4$,then $\frac{1 - \tan^2 \theta}{1 + \tan^2 \theta} = \dots$

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:

Show that $\frac{\cos ^{2}\left(45^{\circ}+\theta\right)+\cos ^{2}\left(45^{\circ}-\theta\right)}{\tan \left(60^{\circ}+\theta\right) \tan \left(30^{\circ}-\theta\right)}=1$

If $\cos \theta = \frac{15}{17}$,then the value of $\operatorname{cosec} \theta + \cot \theta$ is .........

If $\tan A = \cot B$,then $A + B = \ldots$

Simplify $(1+\tan ^{2} \theta)(1-\sin \theta)(1+\sin \theta)$