Embibe Experts Solutions for Chapter: Trigonometric Equations and Inequalities, Exercise 3: EXERCISE-3

Find number of values of $\theta$ in the interval $\left[0,4\pi \right]$ satisfying the equation $\left(1-\tan \theta \right)\left(1+\sin 2\theta \right)=1+\tan \theta$.

Find number of values of $\theta$ in the interval $\left[0,2\pi \right]$ satisfying the equation $\sec 4\theta -\sec 2\theta =2$.

Find number of values of $x$ in the interval $\left[0,2\pi \right]$ satisfying the equation $\cos 3x.{\cos }^{3}x+\sin 3x.{\sin }^{3}x=0$.

If smallest positive value of $x$ and $y$ satisfying equations: $x-y=\frac{\pi }{4}$ and $\cot x+\cot y=2$ are $a$ and $b$ respectively. Find the value of $\frac{a}{b}$.

Find number of values of $\theta$ in the interval $\left[0,\pi \right]$ satisfying the equation $\tan \theta +\tan \left(\theta +\frac{\pi }{3}\right)+\tan \left(\theta +\frac{2\pi }{3}\right)=3$.

Find number of values of $\theta$ in the interval $\left[0,2\pi \right]$ satisfying the equation $\sin 2\theta =\cos 3\theta$.

Find number of values of $\theta$ in the interval $\left[0,\pi \right]$ satisfying the equation $\sin 7\theta =\sin \theta +\sin 3\theta$.

If the smallest positive value of $x$ satisfying $x-y=\frac{\pi }{4}, \cot x+\cot y=2$ is $\frac{a\pi }{12}$, where $a$ is natural number, then the value of $a$ is: