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
$\frac{3}{5}$
$\frac{7}{5}$
$\frac{4}{5}$
$\frac{8}{5}$
Let $f(x) = \cos \sqrt {x,} $ then which of the following is true
The general solution of $a\cos x + b\sin x = c,$ where $a,\,\,b,\,\,c$ are constants
The number of values of $\theta $ in $[0, 2\pi]$ satisfying the equation $2{\sin ^2}\theta = 4 + 3$$\cos \theta $ are
The general solution of $\sin x - \cos x = \sqrt 2 $, for any integer $n$ is
If $4{\sin ^2}\theta + 2(\sqrt 3 + 1)\cos \theta = 4 + \sqrt 3 $, then the general value of $\theta $ is