QJEEM18Maa6e2: JEE Main 2018 Mathematics - Class 11 JEEM18Maa6e2 Solution: The number of solutions of sin3x = cos 2x, in the interval ( π…

Question

Verified Solution • 2025–26 Session moderate

The number of solutions of sin3x = cos 2x, in the interval

(\frac{π}{2}, π)

is :

Accepted Answer

sin 3x = cos 2x

\Rightarrow

3 sin x

-

4 sin³ x = 1

-

2 sin² x

\Rightarrow

4 sin³ x

-

2 sin² x

-

3 sin x + 1 = 0

\Rightarrow

sin x = 1,

\frac{- 2 \pm 2 \sqrt{5}}{8}

In the interval

(\frac{π}{2}, π)

, sin x =

\frac{- 2 + 2 \sqrt{5}}{8}

So, there is only one solution.

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