The value of $\cos 15^\circ - \sin 15^\circ $ is equal to
$\frac{1}{{\sqrt 2 }}$
$\frac{1}{2}$
$ - \frac{1}{{\sqrt 2 }}$
$0$
$\frac{{\tan A + \sec A - 1}}{{\tan A - \sec A + 1}} = $
If $A$ lies in the third quadrant and $3\ tanA - 4 = 0$ , then find the value of $5\ sin\ 2A + 3\ sinA + 4\ cosA$
If $\alpha $ is a root of $25{\cos ^2}\theta + 5\cos \theta - 12 = 0$, $\pi /2 < \alpha < \pi $, then $\sin 2\alpha $ is equal to
$\tan \alpha + 2\tan 2\alpha + 4\tan 4\alpha + 8\cot \,8\alpha = $
$\tan 9^\circ - \tan 27^\circ - \tan 63^\circ + \tan 81^\circ = $