The value of $ \cos ^{3}\left(\frac{\pi}{8}\right) \cdot \cos \left(\frac{3 \pi}{8}\right)+\sin ^{3}\left(\frac{\pi}{8}\right) \cdot \sin \left(\frac{3 \pi}{8}\right)$ is
$\frac{1}{4}$
$\frac{1}{\sqrt{2}}$
$\frac{1}{2\sqrt{2}}$
$\frac{1}{2}$
If $\frac{{5\pi }}{2} < x < 3\pi $, then the value of the expression $\frac{{\sqrt {1 - \sin x} + \sqrt {1 + \sin x} }}{{\sqrt {1 - \sin x} - \sqrt {1 + \sin x} }}$ is
If $2\tan A = 3\tan B,$ then $\frac{{\sin 2B}}{{5 - \cos 2B}}$ is equal to
${(\cos \alpha + \cos \beta )^2} + {(\sin \alpha + \sin \beta )^2} = $
The value of $2 \sin(\frac{\pi}{8}) \sin (\frac{2 \pi}{8}) \sin (\frac{3 \pi}{8}) \sin (\frac{5 \pi}{8}) \sin (\frac{6 \pi}{8}) \sin (\frac{7 \pi}{8})$ is:
If $\frac{{\cos x}}{a} = \frac{{\cos (x + \theta )}}{b} = \frac{{\cos (x + 2\theta )}}{c} = \frac{{\cos (x + 3\theta )}}{d} \, ,$ then $\left( {\frac{{a + c}}{{b + d}}} \right)$ is equal to :-