The sum of solutions in $x \in (0,2\pi )$ of the equation, $4\cos (x).\cos \left( {\frac{\pi }{3} - x} \right).\cos \left( {\frac{\pi }{3} + x} \right) = 1$ is equal to
$\pi $
$2\pi $
$3\pi $
$4\pi $
The general solution of $sin\, x + sin \,5x = sin\, 2x + sin \,4x$ is :
If $\sin 3\alpha = 4\sin \alpha \sin (x + \alpha )\sin (x - \alpha ),$ then $x = $
If equation in variable $\theta, 3 tan(\theta -\alpha) = tan(\theta + \alpha)$, (where $\alpha$ is constant) has no real solution, then $\alpha$ can be (wherever $tan(\theta - \alpha)$ & $tan(\theta + \alpha)$ both are defined)
The real roots of the equation $cos^7x\, +\, sin^4x\, =\, 1$ in the interval $(-\pi, \pi)$ are
The variable $x$ satisfying the equation $\left| {\sin \,x\,\cos \,x} \right| + \sqrt {2 + {{\tan }^2}\,x + {{\cot }^2}\,x} = \sqrt 3$ belongs to the interval