The general solution of $a\cos x + b\sin x = c,$ where $a,\,\,b,\,\,c$ are constants
$x = n\pi + {\cos ^{ - 1}}\left( {\frac{c}{{\sqrt {{a^2} + {b^2}} }}} \right)$
$x = 2n\pi - {\tan ^{ - 1}}\left( {\frac{b}{a}} \right)$
$x = 2n\pi - {\tan ^{ - 1}}\left( {\frac{b}{a}} \right) \pm {\cos ^{ - 1}}\left( {\frac{c}{{\sqrt {{a^2} + {b^2}} }}} \right)$
$x = 2n\pi + {\tan ^{ - 1}}\left( {\frac{b}{a}} \right) \pm {\cos ^{ - 1}}\left( {\frac{c}{{\sqrt {{a^2} + {b^2}} }}} \right)$
The sum of the solutions in $x \in (0,4\pi )$ of the equation $4\sin \frac{x}{3}\left( {\sin \left( {\frac{{\pi + x}}{3}} \right)} \right)\sin \left( {\frac{{2\pi + x}}{3}} \right) = 1$ is
The sum of all $x \in[0, \pi]$ which satisfy the equation $\sin x+\frac{1}{2} \cos x=\sin ^2\left(x+\frac{\pi}{4}\right)$ is
Number of solutions of $8cosx$ = $x$ will be
For which value of $x$ ; $cosx > sinx,$ where $x\, \in \,\,\left( {\frac{\pi }{2}\,,\,\frac{{3\pi }}{2}} \right)$
If ${\tan ^2}\theta - (1 + \sqrt 3 )\tan \theta + \sqrt 3 = 0$, then the general value of $\theta $ is