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

The value of the expression $\left[\operatorname{cosec}(75^{\circ}+\theta)-\sec(15^{\circ}-\theta)-\tan(55^{\circ}+\theta)+\cot(35^{\circ}-\theta)\right]$ is

Prove the following identity,where the angles involved are acute angles for which the expressions are defined:
$\frac{\cos A}{1+\sin A}+\frac{1+\sin A}{\cos A}=2 \sec A$

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

If $\sin \theta + \sin^2 \theta = 1$,then $\cos^2 \theta + \cos^4 \theta = \dots$

$\cot \theta \cdot \tan \theta = \dots$