Question

${\sin }^2\theta {\cos }^3\theta -{\sin }^4\theta \cos \theta \text{is equal}$

• A. $\frac{1}{2}\cos \theta \sin 4\theta$
• B. $\frac{1}{4}\cos \theta \sin 4\theta$
• C. $\frac{1}{2}{\sin }^{2}2\theta$
• D. $\frac{1}{4}\sin \theta \sin 4\theta$

Answer 1

The correct option is D $\frac{1}{4}\sin \theta \sin 4\theta$

$\text{Given}:{\sin }^2\theta {\cos }^3\theta -{\sin }^4\theta \cos \theta ={\sin }^2\theta \cos \theta ({\cos }^2\theta -{\sin }^2\theta )={\sin }^2\theta \cos \theta \cos 2\theta =\frac{1}{2}\sin \theta \sin \theta \cos \theta \cos 2\theta =\frac{1}{2}\sin \theta \sin 2\theta \cos 2\theta =\frac{1}{4}\sin \theta \sin 4\theta$
Hence, The correct answer is option D.