The product $\left(1+\tan 1^{\circ}\right)\left(1+\tan 2^{\circ}\right)\left(1+\tan 3^{\circ}\right)$ $. .\left(1+\tan 45^{\circ}\right)$ equals
$2^{21}$
$2^{22}$
$2^{23}$
$2^{25}$
If $5\tan \theta = 4,$ then $\frac{{5\sin \theta - 3\cos \theta }}{{5\sin \theta + 2\cos \theta }} = $
If $\sin \theta = - \frac{1}{{\sqrt 2 }}$ and $\tan \theta = 1,$ then $\theta $ lies in which quadrant
If $\tan x=\frac{3}{4}, \pi < x < \frac{3 \pi}{2},$ find the value of $\sin \frac{x}{2}, \cos \frac{x}{2}$ and $\tan \frac{x}{2}$
The value of $\sin 10^\circ + \sin 20^\circ + \sin 30^\circ + ... + $ $\sin 360^\circ $ is
Find the value of the trigonometric function $\cot \left(-\frac{15 \pi}{4}\right)$