If $\cos \,\alpha + \cos \,\beta = \frac{3}{2}$ and $\sin \,\alpha + \sin \,\beta = \frac{1}{2}$ and $\theta $ is the the arithmetic mean of $\alpha $ and $\beta $ , then $\sin \,2\theta + \cos \,2\theta $ is equal to
$\frac{3}{5}$
$\frac{7}{5}$
$\frac{4}{5}$
$\frac{8}{5}$
The solution of $\frac{1}{2} +cosx + cos2x + cos3x + cos4x = 0$ is
If $\cos ec\,\theta = \frac{{p + q}}{{p - q}}$ $\left( {p \ne q \ne 0} \right)$, then $\left| {\cot \left( {\frac{\pi }{4} + \frac{\theta }{2}} \right)} \right|$ is equal to
The number of solutions of equation $3cos^2x - 8sinx = 0$ in $[0, 3\pi]$ is
The number of solutions of the equation $\sin \theta+\cos \theta=\sin 2 \theta$ in the interval $[-\pi, \pi]$ is
The equation, $sin^2 \theta - \frac{4}{{{{\sin }^3}\,\,\theta \,\, - \,\,1}} = 1$$ -\frac{4}{{{{\sin }^3}\,\,\theta \,\, - \,\,1}}$ has :