In a right angled triangle the hypotenuse is $2 \sqrt 2$ times the perpendicular drawn from the opposite vertex. Then the other acute angles of the triangle are
$\frac{\pi }{3}$ & $\frac{\pi }{3}$
$\frac{\pi }{8}$ & $\frac{3 \pi }{8}$
$\frac{\pi }{4}$ & $\frac{\pi }{4}$
$\frac{\pi }{5}$ & $\frac{3 \pi }{10}$
$\tan 1^\circ \tan 2^\circ \tan 3^\circ \tan 4^\circ ........\tan 89^\circ = $
If $\cos x + {\cos ^2}x = 1,$ then the value of ${\sin ^2}x + {\sin ^4}x$ is
If $\sin (\alpha - \beta ) = \frac{1}{2}$ and $\cos (\alpha + \beta ) = \frac{1}{2},$ where $\alpha $ and $\beta $ are positive acute angles, then
If $\sin \theta + \cos \theta = m$ and $\sec \theta + {\rm{cosec}}\theta = n$, then $n(m + 1)(m - 1) = $
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