JEE Main 2022 · 29 Jun · Shift 1 · Mathematics Q24

MathematicsInteger+4 / -1Question 24 of 90

The number of elements in the set $S=\left\{\theta\in[-4\pi,4\pi]:3\cos^22\theta+6\cos2\theta-10\cos^2\theta+5=0\right\}$ is ______.

Your answer

Answer and worked solution

Official answer: 32

Simplify with $c=\cos2\theta$ : $3c^2+6c-5(1+c)+5=3c^2+c=0$ , so $c=0$ or $-\frac13$ .

Count. $2\theta\in[-8\pi,8\pi]$ : each value gives 16 solutions.

Answer: 32

JEE Main 2022 · 29 Jun · Shift 1, Mathematics question 24