K. C. Sinha Solutions for Chapter: Trigonometric Equations and Inequations, Exercise 1: EXERCISE

One solution of the equation $4{\cos }^{2}x\sin x-2{\sin }^{2}x=3\sin x$ is

The set of all $x$ in the interval $\left[0,\pi \right]$ for which $2{\sin }^{2}x-3\sin x+1\ge 0$ is

If $\tan \left(\pi \cos \theta \right)=\cot \left(\pi \sin \theta \right)$, then $\cos \left(\theta -\frac{\pi }{4}\right)$ is

The maximum value of $\left(1+\cos x\right)\sin x$ for $0\le x\le \frac{\pi }{2}$ is for

The general value of $\theta$ satisfying $\cot \theta =-\sqrt{3}$ and $\cos \theta =\frac{\sqrt{3}}{2}$ is

The solution of the equation ${\sin }^{6}2x=1+{\cos }^{6}x$ is

The number of solutions of $\sin 2x+\cos 4x=2$ in the interval $\left(0,2\pi \right)$ is

Number of real roots of the equation $\sec \theta +cosec\theta =\sqrt{15}$ lying between $0$ and $\pi$ is