The solution of the equation ${\cos ^2}x - 2\cos x = $ $4\sin x - \sin 2x,$ $\,(0 \le x \le \pi )$ is
$\pi - {\cot ^{ - 1}}\left( {\frac{1}{2}} \right)$
$\pi - {\tan ^{ - 1}}(2)$
$\pi + {\tan ^{ - 1}}\left( { - \frac{1}{2}} \right)$
None of these
The number of integral values of $k$, for which the equation $7\cos x + 5\sin x = 2k + 1$ has a solution, is
Let $S=\left[-\pi, \frac{\pi}{2}\right)-\left\{-\frac{\pi}{2},-\frac{\pi}{4},-\frac{3 \pi}{4}, \frac{\pi}{4}\right\}$. Then the number of elements in the set $=\{\theta \in S : \tan \theta(1+\sqrt{5} \tan (2 \theta))=\sqrt{5}-\tan (2 \theta)\}$ is $...$
Let $f(x) = \cos \sqrt {x,} $ then which of the following is true
The equation $2{\cos ^2}\left( {\frac{x}{2}} \right)\,{\sin ^2}x\, = \,{x^2}\, + \,\frac{1}{{{x^2}}},\,0\,\, \leqslant \,\,x\,\, \leqslant \,\,\frac{\pi }{2}\,\,$ has
Find the principal and general solutions of the equation $\cot x=-\sqrt{3}$