If $f(x) = \frac{\cos^2 x + \sin^4 x}{\sin^2 x + \cos^4 x}$,for $x \in R$,then $f(2002)$ is equal to

If $x=\log _e\left[\cot \left(\frac{\pi}{4}+\theta\right)\right]$ and $\theta \in\left(\frac{-\pi}{4}, \frac{\pi}{4}\right)$,then consider the following statements:
$I$ : $\cosh x=\sec 2 \theta$
$II$ : $\sinh x=-\tan 2 \theta$
Then which one of the following options is true?

The number of ordered pairs $(x, y)$ satisfying the equations $\sin x + \sin y = \sin(x + y)$ and $|x| + |y| = 1$ is

If $\sin \theta + \sin^2 \theta = 1$ and $\cos^{12} \theta + a \cos^{10} \theta + b \cos^8 \theta + c \cos^6 \theta + d = 0$,then:

$\sin \frac{\pi}{16} \sin \frac{3 \pi}{16} \sin \frac{5 \pi}{16} \sin \frac{7 \pi}{16}$ is equal to

If $\sin \theta + \cos \theta = p$ and $\tan \theta + \cot \theta = q$,then $q(p^2 - 1)$ is equal to