If $A$ and $B$ are complimentary angles, then :
$\left( {1\,\, + \,\,\tan \,\frac{A}{2}} \right)\,\,\left( {1\,\, + \,\,\tan \,\frac{B}{2}} \right) = 2$
$\left( {1\,\, + \,\,\cot \,\frac{A}{2}} \right)\,\,\left( {1\,\, + \,\,\cot \,\frac{B}{2}} \right) = 2$
$\left( {1\,\, + \,\,\sec \,\frac{A}{2}} \right)\,\,\left( {1\,\, + \,\,\cos ec\,\frac{B}{2}} \right) = 2$
$\left( {1\,\, - \,\,\tan \,\frac{A}{2}} \right)\,\,\left( {1\,\, - \,\,\tan \,\frac{B}{2}} \right) = 2$
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
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
If $3\cos \theta + 4\sin \theta = 5$ then $3\sin \theta - 4\cos \theta $ is
The sines of two angles of a triangle are equal to $\frac{5}{{13}}$ & $\frac{{99}}{{101}}.$ The cosine of the third angle is :
$\frac{{\tan A + \sec A - 1}}{{\tan A - \sec A + 1}} = $