If $\sec \theta = \frac{13}{5}$,then $\cos \theta = \ldots \ldots \ldots \ldots$

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

Given that $\sin \theta + 2 \cos \theta = 1$,prove that $2 \sin \theta - \cos \theta = 2$.

The value of the expression $\left[\frac{\sin ^{2} 22^{\circ}+\sin ^{2} 68^{\circ}}{\cos ^{2} 22^{\circ}+\cos ^{2} 68^{\circ}}+\sin ^{2} 63^{\circ}+\cos 63^{\circ} \sin 27^{\circ}\right]$ is:

If $\cos A = \frac{4}{5}$,then the value of $\tan A$ is

$2 \sin ^{2} 30^{\circ} \cot 30^{\circ}-3 \cos ^{2} 60^{\circ} \sec ^{2} 30^{\circ} = \dots$