If $\left| {\,a\,{{\sin }^2}\theta + b\sin \theta \cos \theta + c\,{{\cos }^2}\theta - \frac{1}{2}(a + c)\,} \right|\, \le \frac{1}{2}k,$ then ${k^2}$ is equal to
${b^2} + {(a - c)^2}$
${a^2} + {(b - c)^2}$
${c^2} + {(a - b)^2}$
None of these
Find the value of:
$\tan 15^{\circ}$
If $A + B + C = \pi $ and $\cos A = \cos B\,\cos C,$ then $\tan B\,\,\tan C$ is equal to
If ${\tan ^2}\alpha {\tan ^2}\beta + {\tan ^2}\beta {\tan ^2}\gamma + {\tan ^2}\gamma {\tan ^2}\alpha $$ + 2{\tan ^2}\alpha {\tan ^2}\beta {\tan ^2}\gamma = 1,$ then the value of ${\sin ^2}\alpha + {\sin ^2}\beta + {\sin ^2}\gamma $ is
If $\sin x + {\rm{cosec}}\,x = 2,$ then $sin^n x + cosec^n x$ is equal to
$\sin \left( {\frac{\pi }{{10}}} \right)\sin \left( {\frac{{3\pi }}{{10}}} \right) = $