Embibe Experts Solutions for Chapter: Trigonometric Equations and Inequations, Exercise 1: Exercise 1

If $\cos 3x+\sin \left(2x-\frac{7\pi }{6}\right)=-2,$ then $x$ is equal to $(k\in Z)$

Sum of all the solutions in $[0,4\pi ]$ of the equation $\tan x+\cot x+1=\cos \left(x+\frac{\pi }{4}\right)$ is

What is/are the solution(s) of the trigonometric equation $cosecx+\cot x=\sqrt{3}$, where $0<x<2\pi ?$

The smallest positive $x$ satisfying the equation ${\log }_{\cos x}\sin x+{\log }_{\sin x}\cos x=2$ is

The general solution of the equaiton ${\sin }^{100}x-{\cos }^{100}x=1$ is

If $4{\sin }^2\theta =1,$ where $0<\theta <2\pi ,$ how many values does $\theta$ take$?$

The number of solutions of $\sum _{r=1}^5\cos rx=5$ in the interval $[0,2\pi ]$ is

Let $\alpha$ and $\beta$ be any two positive values of $x$ for which $2\cos x, \left|\cos x\right|$ and $1-3{\cos }^{2}x$ are in $\mathrm{G}.\mathrm{P}.$ The minimum value of $|\alpha -\beta |$ is