Trigonometric Equations

The set of all $x$ for which $\sin x \leq x$ is

The smallest positive root of the equation $\tan x-x=0$ lies in the interval

$\begin{aligned} & \text { If } x: y: z=\tan \left(\frac{\pi}{15}+\alpha\right): \tan \left(\frac{\pi}{15}+\beta\right): \\ & \tan \left(\frac{\pi}{15}+\gamma\right), \operatorname{then} \frac{z+x}{z-x} \sin…

The extreme values of $4 \cos \left(x^2\right) \cos \left(\frac{\pi}{3}+x^2\right) \cos \left(\frac{\pi}{3}-x^2\right)$ over $R$, are

Number of solutions of the trigonometric equation $2 \tan 2 \theta-\cot 2 \theta+1=0$ lying in the interval $[0, \pi]$ is

If the general solution of $\sin 5 x=\cos 2 x$ is of the form $a_n \cdot \frac{\pi}{2}$ for $n=0, \pm 1, \pm 2, \ldots .$. , then $a_n=$

If $x \neq(2 n+1) \frac{\pi}{4}$, then the general solution of $\cos x+\cos 3 x=\sin x+\sin 3 x$ is

The general solution of the equation $\sin ^2 \theta+3 \cos ^2 \theta=5 \sin \theta$ is

The general solution of $4 \cos 2 x-4 \sqrt{3} \sin 2 x+\cos 3 x-$ $\sqrt{\sin 3 x+\cos x-\sqrt{3} \sin x}=0$

Find the general solution of ' \(\sin x+\sin 2 x\) \(+\sin 3 x=\cos x+\cos 2 x+\cos 3 x^{\prime}\)

If $\frac{1}{6} \sin \theta, \cos \theta$ and $\tan \theta$ are in geometric progression, then the solution set of $\theta$ is

The set of solutions of the equation $(\sqrt{3}-1) \sin \theta+(\sqrt{3}+1) \cos \theta=2$ is