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
The angle subtended at the centre of a circle of radius $3$ metres by an arc of length $1$ metre is equal to
If $\sin x + {\sin ^2}x = 1$, then the value of ${\cos ^{12}}x + 3{\cos ^{10}}x + 3{\cos ^8}x + {\cos ^6}x - 2$ is equal to
If $\theta $ and $\phi $ are angles in the $1^{st}$ quadrant such that $\tan \theta = 1/7$ and $\sin \phi = 1/\sqrt {10} $.Then
Find the values of other five trigonometric functions if $\cos x=-\frac{1}{2}, x$ lies in third quadrant.
If $\sin x + {\rm{cosec}}\,x = 2,$ then $sin^n x + cosec^n x$ is equal to