Trigonometric Equation - JEE Advanced Previous Year Questions with Solutions

Q. The number of values of $\theta$ in the interval $\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)$ such that $\theta \neq \frac{n \pi}{5}$ for $n=0, \pm 1, \pm 2$ and $\tan \theta=\cot 5 \theta$ as well as $\sin 2 \theta=\cos 4 \theta,$ is [JEE 2010, 3]

Q. The positive integer value of n > 3 satisfying the equation $\frac{1}{\sin \left(\frac{\pi}{\mathrm{n}}\right)}=\frac{1}{\sin \left(\frac{2 \pi}{\mathrm{n}}\right)}+\frac{1}{\sin \left(\frac{3 \pi}{\mathrm{n}}\right)}$ is [JEE 2011, 4]

Q. Let $\theta, \varphi \in[0,2 \pi]$ be such that $2 \cos \theta(1-\sin \varphi)=\sin ^{2} \theta\left(\tan \frac{\theta}{2}+\cot \frac{\theta}{2}\right) \cos \varphi-1, \tan (2 \pi-\theta)>0$ and $-1<\sin \theta<-\frac{\sqrt{3}}{2} .$ Then $\varphi$ cannot satisfy- (A) $0<\varphi<\frac{\pi}{2}$ (B) $\frac{\pi}{2}<\varphi<\frac{4 \pi}{3}$ (C) $\frac{4 \pi}{3}<\varphi<\frac{3 \pi}{2}$ (D) $\frac{3 \pi}{2}<\varphi<2 \pi$ [JEE 2012, 4M]

Q. For $\mathrm{x} \in(0, \pi),$ the equation $\sin \mathrm{x}+2 \sin 2 \mathrm{x}-\sin 3 \mathrm{x}=3 \mathrm{has}$ (A) infinitely many solutions (B) three solutions (C) one solution (D) no solution [JEE(Advanced)-2014, 3(–1)]

Q. The number of distinct solutions of equation $\frac{5}{4} \cos ^{2} 2 x+\cos ^{4} x+\sin ^{4} x+\cos ^{6} x+\sin ^{6} x=2$ in the interval $[0,2 \pi]$ is [JEE 2015, 4M, –0M]

Q. Let $S=\left\{x \in(-\pi, \pi): x \neq 0, \pm \frac{\pi}{2}\right\} .$ The sum of all distinct solution of the equation $\sqrt{3} \sec x+\csc x+2(\tan x-\cot x)=0$ in the set $S$ is equal to $-$ (A) $-\frac{7 \pi}{9}$ (B) $-\frac{2 \pi}{9}$ (C) 0 (D) $\frac{5 \pi}{9}$ [JEE(Advanced)-2016]

Q. Let $a, b, c$ be three non-zero real numbers such that the equation $\sqrt{3} a \cos x+2 b \sin x=c, \quad x$ $\in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ has two distinct real roots $\alpha$ and $\beta$ with $\alpha+\beta=\frac{\pi}{3} .$ Then the value of $\frac{b}{a}$ is $-$ $=$ [JEE(Advanced)-2018]