The total number of solution of $sin^4x + cos^4x = sinx\, cosx$ in $[0, 2\pi ]$ is equal to
$2$
$4$
$6$
none of these
If $tan(\pi sin \theta)$ $= cot(\pi cos \theta)$, then $\left| {\cot \left( {\theta - \frac{\pi }{4}} \right)} \right|$ is -
If $2{\tan ^2}\theta = {\sec ^2}\theta ,$ then the general value of $\theta $ is
If $1 + \cot \theta = {\rm{cosec}}\theta $, then the general value of $\theta $ is
Let $X=\{x \in R: \cos (\sin x)=\sin (\cos x)\} .$ The number of elements in $X$ is
If $\tan \theta - \sqrt 2 \sec \theta = \sqrt 3 $, then the general value of $\theta $ is