If $\left| {\cos \,\theta \,\left\{ {\sin \theta + \sqrt {{{\sin }^2}\theta + {{\sin }^2}\alpha } } \right\}\,} \right|\, \le k,$ then the value of $k$ is
$\sqrt {1 + {{\cos }^2}\alpha } $
$\sqrt {1 + {{\sin }^2}\alpha } $
$\sqrt {2 + {{\sin }^2}\alpha } $
$\sqrt {2 + {{\cos }^2}\alpha } $
If $\sin (\alpha - \beta ) = \frac{1}{2}$ and $\cos (\alpha + \beta ) = \frac{1}{2},$ where $\alpha $ and $\beta $ are positive acute angles, then
The value of $k$, for which ${(\cos x + \sin x)^2} + k\,\sin x\cos x - 1 = 0$ is an identity, is
If $\cos x=-\frac{3}{5}, x$ lies in the third quadrant, find the values of other five trigonometric functions.
Find the value of the trigonometric function $\sin \left(-\frac{11 \pi}{3}\right)$
The value of $\cos A - \sin A$ when $A = \frac{{5\pi }}{4},$ is