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

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

JEE MainJEE Main 2022Trigonometric Functions

Solution:

$\sin ^{2} x+\sin x-1=0$
$\sin x=\frac{-1+\sqrt{5}}{2}=+v e$
Only $4$ roots