The number of solution of the given equation $a\sin x + b\cos x = c$ , where $|c|\, > \,\sqrt {{a^2} + {b^2}} ,$ is

One root of the equation $\cos x - x + \frac{1}{2} = 0$ lies in the interval

Number of principal solution of the equation $tan \,3x - tan \,2x - tan\, x = 0$, is

The real roots of the equation $cos^7x\,  +\,  sin^4x\,  =\,  1$  in the interval $(-\pi, \pi)$ are

Let $S=\left\{x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right): 9^{1-\tan ^2 x}+9^{\tan ^2 x}=10\right\}$ and $\beta=\sum_{x \in S} \tan ^2\left(\frac{x}{3}\right)$, then $\frac{1}{6}(\beta-14)^2$ is equal to

The number of solutions to the equation $\cos ^4 x+\frac{1}{\cos ^2 x}=\sin ^4 x+\frac{1}{\sin ^2 x}$ in the interval $[0,2 \pi]$ is