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

If $\sec 4A = \operatorname{cosec}(A - 20^\circ)$,where $4A$ is an acute angle,then the value of $A$ is $\ldots \ldots \ldots \ldots .$ (in $^\circ$)

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

If $\tan \theta + \sec \theta = l$,then prove that $\sec \theta = \frac{l^{2} + 1}{2l}$.

Given that $\alpha + \beta = 90^{\circ}$,show that $\sqrt{\cos \alpha \operatorname{cosec} \beta - \cos \alpha \sin \beta} = \sin \alpha$.

$\tan (90^\circ - \theta) = \ldots \ldots \ldots$