If $\tan (\pi \cos \theta ) = \cot (\pi \sin \theta )$, then $\sin \left( {\theta + \frac{\pi }{4}} \right)$ equals
$\frac{1}{{\sqrt 2 }}$
$\frac{1}{2}$
$\frac{1}{{2\sqrt 2 }}$
$\frac{{\sqrt 3 }}{2}$
The equation $3\cos x + 4\sin x = 6$ has
The smallest positive angle which satisfies the equation $2{\sin ^2}\theta + \sqrt 3 \cos \theta + 1 = 0$, is
The number of elements in the set $S =\left\{\theta \in[0,2 \pi]: 3 \cos ^4 \theta-5 \cos ^2 \theta-2 \sin ^2 \theta+2=0\right\}$ is $...........$.
The number of solutions of $|\cos x|=\sin x$, such that $-4 \pi \leq x \leq 4 \pi$ is.
If $\cos p\theta = \cos q\theta ,p \ne q$, then