${(\cos \alpha + \cos \beta )^2} + {(\sin \alpha + \sin \beta )^2} = $
$4{\cos ^2}\frac{{\alpha - \beta }}{2}$
$4{\sin ^2}\frac{{\alpha - \beta }}{2}$
$4{\cos ^2}\frac{{\alpha + \beta }}{2}$
$4{\sin ^2}\frac{{\alpha + \beta }}{2}$
$\cos \frac{\pi }{7}\cos \frac{{2\pi }}{7}\cos \frac{{3\pi }}{7} =$
$\cos \frac{\pi }{5}\cos \frac{{2\pi }}{5}\cos \frac{{4\pi }}{5}\cos \frac{{8\pi }}{5} = $
$A, B, C$ are the angles of a triangle, then ${\sin ^2}A + {\sin ^2}B + {\sin ^2}C - 2\cos A\,\cos B\,\cos C = $
Number of values of $ x \in \left[ {0,2\pi } \right]$ satisfying the equation $cotx - cosx = 1 - cotx. cosx$
The value of $\sum_{r-1}^{18} cos^2(5r)^o,$ where $x^o $ denotes the $x$ degree, is equals to