The solution of the equation $\sec \theta - {\rm{cosec}}\theta = \frac{4}{3}$ is
$\frac{1}{2}[n\pi + {( - 1)^n}{\sin ^{ - 1}}(3/4)]$
$n\pi + {( - 1)^n}{\sin ^{ - 1}}(3/4)$
$\frac{{n\pi }}{2} + {( - 1)^n}{\sin ^{ - 1}}(3/4)$
None of these
Number of solutions of equation $sgn(sin x) = sin^2x + 2sinx + sgn(sin^2x)$ in $\left[ { - \frac{{5\pi }}{2},\frac{{7\pi }}{2}} \right]$ is
(where $sgn(.)$ denotes signum function) -
If $\sin \theta + \cos \theta = 1$ then the general value of $\theta $ is
The set of all values of $\lambda$ for which the equation $\cos ^2 2 x-2 \sin ^4 x-2 \cos ^2 x=\lambda$
If the sum of solutions of the system of equations $2 \sin ^{2} \theta-\cos 2 \theta=0$ and $2 \cos ^{2} \theta+3 \sin \theta=0$ in the interval $[0,2 \pi]$ is $k \pi$, then $k$ is equal to.
Find the principal and general solutions of the equation $\sec x=2$