If $\tan \theta = \frac{5}{12}$,then $\cos \theta = \ldots$

State whether the following is 'True' or 'False' and justify your answer:
If $\cos A + \cos^2 A = 1$,then $\sin^2 A + \sin^4 A = 1$.

If $a \sin \theta + b \cos \theta = c$,then prove that $a \cos \theta - b \sin \theta = \pm \sqrt{a^2 + b^2 - c^2}$,given $a^2 + b^2 \geq c^2$.

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

If $3 \theta$ is the measure of an acute angle and $\sin 3 \theta = \cos (\theta - 26^{\circ})$,then the value of $\theta$ is $\ldots \ldots \ldots \ldots$ (in $^{\circ}$)

$(1-\cos \theta)(1+\cos \theta) = \dots$