$(m + 2)\sin \theta + (2m - 1)\cos \theta = 2m + 1,$ if
$\tan \theta = \frac{3}{4}$
$\tan \theta = \frac{4}{3}$
$\tan \theta = \frac{{2m}}{{{m^2} + 1}}$
None of these
If $\sec \theta + \tan \theta = p,$ then $\tan \theta $ is equal to
If $A = 130^\circ $ and $x = \sin A + \cos A,$ then
Prove that $\cos ^{2} x+\cos ^{2}\left(x+\frac{\pi}{3}\right)+\cos ^{2}\left(x-\frac{\pi}{3}\right)=\frac{3}{2}$
If $2y\,\cos \theta = x\sin \,\theta {\rm{ and }}2x\sec \theta - y\,{\rm{cosec}}\,\theta = 3,$ then ${x^2} + 4{y^2} = $
Let the function $:(0, \pi) \rightarrow R$ be defined by
$f (\theta)=(\sin \theta+\cos \theta)^2+(\sin \theta-\cos \theta)^4$
Suppose the function $f$ has a local minimum at $\theta$ precisely when $\theta \in\left\{\lambda_1 \pi, \ldots, \lambda_{ T } \pi\right\}$, where $0<\lambda_1<\cdots<\lambda_r<1$. Then the value of $\lambda_1+\cdots+\lambda_r$ is. . . . .