For $n \in Z$ , the general solution of the equation
$(\sqrt 3 - 1)\,\sin \,\theta \, + \,(\sqrt 3 + 1)\,\cos \theta \, = \,2$ is
$\theta \, = \,2n\pi \, \pm \,\frac{\pi }{4}\, + \,\frac{\pi }{{12}}$
$\theta \, = \,n\pi \, + {( - 1)^\pi }\,\frac{\pi }{4}\, + \,\frac{\pi }{{12}}$
$\theta \, = \,2n\pi \, \pm \,\frac{\pi }{4}\, - \,\frac{\pi }{{12}}$
$\theta \, = \,n\pi \, + {( - 1)^\pi }\,\frac{\pi }{4}\, - \,\frac{\pi }{{12}}$
The number of solutions of the equation $32^{\tan ^{2} x}+32^{\sec ^{2} x}=81,0 \leq x \leq \frac{\pi}{4}$ is :
The general solution of $\sin x - 3\sin 2x + \sin 3x = $ $\cos x - 3\cos 2x + \cos 3x$ is
The general solution of $a\cos x + b\sin x = c,$ where $a,\,\,b,\,\,c$ are constants
The number of solutions of $sin \,3x\, = cos\, 2x$ , in the interval $\left( {\frac{\pi }{2},\pi } \right)$ is
Number of solution $(s)$ of equation $cosec\, \theta -cot \,\theta = 1$ in $[0,2 \pi]$ is-