Q53 / 90 · JEE Main 2022 (29 Jun Shift 2) · Mathematics

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

Correct answer: 4

Solution

Given, $\sin x = \cos^{2} x$

$\Rightarrow \sin x = 1 - \sin^{2} x$

$\Rightarrow \sin^{2} x + \sin x - 1 = 0$

$\Rightarrow \sin x = \frac{(- 1 \pm \sqrt{5})}{2}$

$\Rightarrow \sin x = \frac{(\sqrt{5} - 1)}{2}$

Now plotting the graph we get,

$\Rightarrow$ Now by graph number of solutions in $(0, 10) = 4$

Hence, the correct answer is 4.