JEE Main 2022 · 29 Jun · Shift 2 · Mathematics Q24

MathematicsInteger+4 / -1Question 24 of 90

The number of solutions of the equation $\sin x=\cos^2x$ in the interval $(0,10)$ is ______.

Your answer

Answer and worked solution

Official answer: 4

Quadratic. $\sin^2x+\sin x-1=0$ gives $\sin x=\frac{\sqrt5-1}2\approx0.618$ .

In $(0,10)$ . Two solutions in $(0,\pi)$ and two in $(2\pi,3\pi)$ (both below 10, since the larger is $3\pi-0.67\approx8.75$ ). Total 4.

Answer: 4

JEE Main 2022 · 29 Jun · Shift 2, Mathematics question 24