Question

What Is the maximum value of $\sin 3\theta \cos 2\theta +\cos 3\theta \sin 2\theta$ ?

• A. I
• B. 2
• C. 4
• D. 10

Answer 1

Answer: (A)

I

We know that $\sin (A+B)=\sin A\cos B+\sin B\cos A$

Substituting $A=3\theta$ and $B=2\theta$ we get,

$\sin (2\theta +3\theta )=\sin 2\theta Cos3\theta +\sin 3\theta Cos2\theta$

$\Rightarrow \sin 5\theta =\sin 2\theta Cos3\theta +\sin 3\theta Cos2\theta$

Maximum value of $\sin 5\theta$ is $1.$