Question

If $x = \sin 2\theta \cos 3\theta$, $y = \sin 3\theta \cos 2\theta$, then $\frac{dy}{dx} =$

• A. $\frac{2 \cos 5\theta+\sin 3\theta \sin 2\theta}{2 \cos 5\theta-\cos 3\theta \cos 2\theta}$
• B. $\frac{2 \cos 5\theta-\sin 3\theta \sin 2\theta}{2 \cos 5\theta+\cos 3\theta \cos 2\theta}$
• C. $\frac{2 \cos 5\theta+\cos 3\theta \cos 2\theta}{2 \cos 5\theta-\sin 3\theta \sin 2\theta}$
• D. $\frac{2 \cos 5\theta-\sin 3\theta \sin 2\theta}{2 \cos 5\theta-\cos 3\theta \cos 2\theta}$

Hint:

When differentiating parametric equations like \(x = \sin A \cos B\), \(y = \sin B \cos A\), it helps to first convert products into sums using the identity: \(\sin A \cos B = \frac{1}{2}[\sin(A+B)+\sin(A-B)]\). Then differentiate and simplify using trigonometric addition formulas to match standard forms.

Answer 1

The Correct Option is C