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 

  • [JEE MAIN 2015]
  • A

    $\frac{3}{5}$

  • B

    $\frac{7}{5}$

  • C

    $\frac{4}{5}$

  • D

    $\frac{8}{5}$

Similar Questions

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