If $A$ and $B$ are complimentary angles, then :
$\left( {1\,\, + \,\,\tan \,\frac{A}{2}} \right)\,\,\left( {1\,\, + \,\,\tan \,\frac{B}{2}} \right) = 2$
$\left( {1\,\, + \,\,\cot \,\frac{A}{2}} \right)\,\,\left( {1\,\, + \,\,\cot \,\frac{B}{2}} \right) = 2$
$\left( {1\,\, + \,\,\sec \,\frac{A}{2}} \right)\,\,\left( {1\,\, + \,\,\cos ec\,\frac{B}{2}} \right) = 2$
$\left( {1\,\, - \,\,\tan \,\frac{A}{2}} \right)\,\,\left( {1\,\, - \,\,\tan \,\frac{B}{2}} \right) = 2$
$\tan 9^\circ - \tan 27^\circ - \tan 63^\circ + \tan 81^\circ = $
${(\cos \alpha + \cos \beta )^2} + {(\sin \alpha + \sin \beta )^2} = $
$\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 = $
If $x\, sin \theta = y\, sin \, \left( {\theta \,\, + \,\,\frac{{2\,\pi }}{3}} \right) = z\, sin \, \left( {\theta \,\, + \,\,\frac{{4\,\pi }}{3}} \right)$ then :