Let $S_1,S_2$ and $S_3$ be three circles of unit radius which touch each other externally. The common tangent to each pair of circles are drawn and extended so that they can intersect and form a triangle $ABC$ with circumradius $R,$ then $R$ is equal to
$4+2\sqrt 3$
$2(1+\frac{1}{\sqrt 3})$
$4(1+\sqrt 3)$
$\frac{3(1+\sqrt 3)}{2}$
$\cos 15^\circ = $
If $(\sec \alpha + \tan \alpha )(\sec \beta + \tan \beta )(\sec \gamma + \tan \gamma )$$ = \tan \alpha \tan \beta \tan \gamma $, then $(\sec \alpha - \tan \alpha )(\sec \beta - \tan \beta )$$(\sec \gamma - \tan \gamma ) = $
If $\cos x + {\cos ^2}x = 1,$ then the value of ${\sin ^2}x + {\sin ^4}x$ is
Find the angle in radian through which a pendulum swings if its length is $75\, cm$ and the tip describes an arc of length.
$15\,cm$
If $\tan \theta + \sec \theta = {e^x},$ then $\cos \theta $ equals