If $\cos \theta = \frac{1}{\sqrt{2}},$ then $\theta = \ldots$ (in $^\circ$)

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

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

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

Which of the following is true for some $\theta$ (where,$0 < \theta < 90^{\circ}$)?

If $\cos 9 \alpha = \sin \alpha$ and $9 \alpha < 90^{\circ},$ then the value of $\tan 5 \alpha$ is