The equation $3{\sin ^2}x + 10\cos x - 6 = 0$ is satisfied, if
$x = n\pi \pm {\cos ^{ - 1}}(1/3)$
$x = 2n\pi \pm {\cos ^{ - 1}}(1/3)$
$x = n\pi \pm {\cos ^{ - 1}}(1/6)$
$x = 2n\pi \pm {\cos ^{ - 1}}(1/6)$
The number of real numbers $\lambda$ for which the equality $\frac{\sin (\lambda \alpha) \quad \cos (\lambda \alpha)}{\sin \alpha}=\lambda-1$,holds for all real $\alpha$ which are not integral multiples of $\pi / 2$ is
The number of roots of the equation $\cos ^7 \theta-\sin ^4 \theta=1$ that lie in the interval $[0,2 \pi]$ is
If $\cos p\theta = \cos q\theta ,p \ne q$, then
The sum of the solutions in $x \in (0,4\pi )$ of the equation $4\sin \frac{x}{3}\left( {\sin \left( {\frac{{\pi + x}}{3}} \right)} \right)\sin \left( {\frac{{2\pi + x}}{3}} \right) = 1$ is
If $0 \le x < 2\pi $ , then the number of real values of $x,$ which satisfy the equation $\cos x + \cos 2x + \cos 3x + \cos 4x = 0$ is . . .