$\frac{1}{\tan ^{2} \theta}+1 = \dots$

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

Prove that,
$\frac{\sin \theta}{1+\cos \theta}+\frac{1+\cos \theta}{\sin \theta}=2 \operatorname{cosec} \theta$

$\tan (65^\circ - \theta) - \cot (25^\circ + \theta) - \sec (55^\circ - \theta) + \operatorname{cosec}(35^\circ + \theta) = \ldots \ldots \ldots \ldots$ (where,$0 < \theta < 25^\circ$)

The simplification of $\frac{\cos (90^{\circ}- A ) \sin (90^{\circ}- A )}{\tan (90^{\circ}- A )}$ is .......

If $\tan ^{2} \theta = \sin ^{2} \theta + \cos ^{2} \theta$,then $\theta = \ldots$ (in $^{\circ}$)