If $3 \sin \theta = 4 \cos \theta$,then $\tan \theta = \ldots$

If $\tan \theta = \frac{4}{3}$,then $\frac{5 \sin \theta + 2 \cos \theta}{3 \sin \theta - \cos \theta} = \ldots \ldots$

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

Given that $\sin \theta = \frac{a}{b},$ then $\cos \theta$ is equal to

$2A$ is the measure of an acute angle and $\sec 2A = \operatorname{cosec}(A - 42^\circ)$,then the value of $A$ is $\ldots \ldots \ldots \ldots$ (in $^\circ$)

Prove that:
If $\tan A = \frac{3}{4},$ then $\sin A \cos A = \frac{12}{25}$