If $\sec \theta + \tan \theta = p,$ then $\tan \theta $ is equal to
$\frac{{2p}}{{{p^2} - 1}}$
$\frac{{{p^2} - 1}}{{2p}}$
$\frac{{{p^2} + 1}}{{2p}}$
$\frac{{2p}}{{{p^2} + 1}}$
The angle subtended at the centre of a circle of radius $3$ metres by an arc of length $1$ metre is equal to
Prove that: $(\cos x-\cos y)^{2}+(\sin x-\sin y)^{2}=4 \sin ^{2} \frac{x-y}{2}$
If $\sin \theta + {\rm{cosec}}\theta = {\rm{2}}$, then ${\sin ^2}\theta + {\rm{cose}}{{\rm{c}}^{\rm{2}}}\theta = $
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) = $