$4 \,\,sin5^o \,\,sin55^o \,\,sin65^o$ has the values equal to
$\frac{{\sqrt 3 + 1}}{{2\sqrt 2 }}$
$\frac{{\sqrt 3 - 1}}{{2\sqrt 2 }}$
$\frac{{\sqrt 3 - 1}}{{\sqrt 2 }}$
$\frac{{3\left( {\sqrt 3 - 1} \right)}}{{2\sqrt 2 }}$
If ${\tan ^2}\theta = 2{\tan ^2}\phi + 1,$ then $\cos 2\theta + {\sin ^2}\phi $ equals
If $A, B, C$ are acute positive angles such that $A + B + C = \pi $ and $\cot A\,\cot \,B\,\cot \,C = K,$ then
Let $\frac{\pi}{2} < x < \pi$ be such that $\cot x=\frac{-5}{\sqrt{11}}$. Then $\left(\sin \frac{11 x}{2}\right)(\sin 6 x-\cos 6 x)+\left(\cos \frac{11 x}{2}\right)(\sin 6 x+\cos 6 x)$ is equal to
${\rm{cosec }}A - 2\cot 2A\cos A = $
Prove that $\frac{\cos 9 x-\cos 5 x}{\sin 17 x-\sin 3 x}=-\frac{\sin 2 x}{\cos 10 x}$