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

The number of solutions of the equation sin x=cos2 x in the interval 0, 10 is ______.

Solution

Given, sinx=cos2x

⇒sinx=1-sin2x

⇒  sin2x+sinx-1=0

⇒ sinx=-1±52

⇒  sinx=5-12

Now plotting the graph we get,

⇒ Now by graph number of solutions in 0,10=4

Asked in: JEE Main 2022 (29 Jun Shift 2)

Practice more Trigonometric Equations questions on Aicharya