If $cos A = {3\over 4} , $ then $32\sin \left( {\frac{A}{2}} \right)\sin \left( {\frac{{5A}}{2}} \right) = $

The sines of two angles of a triangle are equal to $\frac{5}{{13}}$ & $\frac{{99}}{{101}}.$ The cosine of the third angle is :

$\cos A + \cos (240^\circ + A) + \cos (240^\circ - A) = $

If $x = sec\, \phi - tan\, \phi$ & $y = cosec\, \phi + cot\, \phi$ then :

If $cosA + cosB = cosC,\ sinA + sinB = sinC$ then the value of expression $\frac{{\sin \left( {A + B} \right)}}{{\sin 2C}}$ is

$\tan 9^\circ - \tan 27^\circ - \tan 63^\circ + \tan 81^\circ = $