Find the value of the trigonometric function $\cot \left(-\frac{15 \pi}{4}\right)$.

Find the degree measure corresponding to the following radian measure (Use $\pi = \frac{22}{7}$): $\frac{7 \pi}{6}$ (in $^{\circ}$)

$1+\sec ^2 x \sin ^2 x=$

Which of the following is true?

The values of $x$ in $\left(0, \frac{\pi}{2}\right)$ satisfying the equation $\sin x \cos x = \frac{1}{4}$ are $.......$

The expression $\frac{\tan \left( \frac{3\pi}{2} - \alpha \right) \cos \left( \frac{3\pi}{2} - \alpha \right)}{\cos (2\pi - \alpha )} + \cos \left( \alpha - \frac{\pi}{2} \right) \sin (\pi - \alpha ) + \cos (\pi + \alpha ) \sin \left( \alpha - \frac{\pi}{2} \right)$ when simplified reduces to: