${\rm{cosec }}A - 2\cot 2A\cos A = $
$2\sin A$
$\sec A$
$2\cos A\cot A$
None of these
The value of the expression $(sinx + cosecx)^2 + (cosx + secx)^2 - ( tanx + cotx)^2$ wherever defined is equal to
$\sin {20^o}\,\sin {40^o}\,\sin {60^o}\,\sin {80^o} = $
If $\cos A = \cos B\,\,\cos C$and $A + B + C = \pi ,$ then the value of $\cot \,B\,\cot \,C$ is
If ${\rm{cosec}}\theta = \frac{{p + q}}{{p - q}},$ then $\cot \,\left( {\frac{\pi }{4} + \frac{\theta }{2}} \right) = $
If $cosA + cosB = cosC,\ sinA + sinB = sinC$ then the value of expression $\frac{{\sin \left( {A + B} \right)}}{{\sin 2C}}$ is