If $\tan ^{2} \theta = \sin ^{2} \theta + \cos ^{2} \theta$ and $0 < \theta < 90^{\circ}$,then the value of $\theta$ is ...... (in $^{\circ}$)

If $\sin A + \sin^2 A = 1$,then the value of the expression $(\cos^2 A + \cos^4 A)$ is

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

In $\Delta ABC$,$m \angle C = 90^{\circ}$ and $\cos B = \frac{1}{2}$,then $\operatorname{cosec} A = \ldots$

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 $\sin \theta + \cos \theta = p$ and $\sec \theta + \operatorname{cosec} \theta = q,$ then prove that $q(p^2 - 1) = 2p$.