If $\tan \theta = t,$ then $\tan 2\theta + \sec 2\theta = $
$\frac{{1 + t}}{{1 - t}}$
$\frac{{1 - t}}{{1 + t}}$
$\frac{{2t}}{{1 - t}}$
$\frac{{2t}}{{1 + t}}$
If $A + B + C = \frac{{3\pi }}{2},$ then $\cos 2A + \cos 2B + \cos 2C = $
$\frac{{\sin \theta + \sin 2\theta }}{{1 + \cos \theta + \cos 2\theta }} = $
If $x + \frac{1}{x} = 2\,\cos \theta ,$ then ${x^3} + \frac{1}{{{x^3}}} = $
$A, B, C$ are the angles of a triangle, then ${\sin ^2}A + {\sin ^2}B + {\sin ^2}C - 2\cos A\,\cos B\,\cos C = $
If a $cos^3 \alpha + 3a \,cos\, \alpha \, sin^2\, \alpha = m$ and $asin^3\, \alpha + 3a \, cos^2\, \alpha \,sin\, \alpha = n$ . Then $(m + n)^{2/3} + (m - n)^{2/3}$ is equal to :