Mathematics

Trigonometric Functions and Equations

Appeared 7 times across 2 years of JEE Main papers — about 3.5 questions a year. Every one of them is below, with a full worked solution.

Questions per year

1’19

6’24

01Easy7×since 2019Q5626

If 0

\le

x <

{\pi \over 2}

, then the number of values of x for which sin x

-

sin 2x + sin 3x = 0, is :

02Medium7×since 2019Q5627

The number of solutions of the equation

4 \sin ^2 x-4 \cos ^3 x+9-4 \cos x=0 ; x \in[-2 \pi, 2 \pi]

is :

03Medium7×since 2019Q5628

2 \tan ^2 \theta-5 \sec \theta=1

has exactly 7 solutions in the interval

\left[0, \frac{n \pi}{2}\right]

, for the least value of

n \in \mathbf{N}

, then

\sum_\limits{k=1}^n \frac{k}{2^k}

is equal to:

04Easy7×since 2019Q5629

\alpha,-\frac{\pi}{2}<\alpha<\frac{\pi}{2}

is the solution of

4 \cos \theta+5 \sin \theta=1

, then the value of

\tan \alpha

05Easy7×since 2019Q5630

The sum of the solutions

x \in \mathbb{R}

of the equation

\frac{3 \cos 2 x+\cos ^3 2 x}{\cos ^6 x-\sin ^6 x}=x^3-x^2+6

06Easy7×since 2019Q5631

2 \sin ^3 x+\sin 2 x \cos x+4 \sin x-4=0

has exactly 3 solutions in the interval

\left[0, \frac{\mathrm{n} \pi}{2}\right], \mathrm{n} \in \mathrm{N}

, then the roots of the equation

x^2+\mathrm{n} x+(\mathrm{n}-3)=0

belong to :

07Easy7×since 2019Q5632

Let

|\cos \theta \cos (60-\theta) \cos (60+\theta)| \leq \frac{1}{8}, \theta \epsilon[0,2 \pi]

. Then, the sum of all

\theta \in[0,2 \pi]

, where

\cos 3 \theta

attains its maximum value, is :