Choose the one alternative that best completes the statement or answers the question.
Complete the identity.
-$\sin \theta \cos ^ { 3 } \theta + \sin ^ { 3 } \theta \cos \theta =$ ?
A) $\frac { 1 } { 2 } \sin ( 2 \theta ) \cos ( 2 \theta )$
B) $\frac { 1 } { 2 } \sin ( 2 \theta )$
C) $\frac { 1 } { 4 } \sin ^ { 2 } ( 2 \theta )$
D) $\frac { 1 } { 6 } \sin ( 3 \theta ) \sin ( 2 \theta )$

Question

Quizplus · Accepted Answer

This expression can be simplified using trigonometric identities. Factor out $\sin \theta \cos \theta$, giving $\sin \theta \cos \theta (\cos^2 \theta + \sin^2 \theta)$. Since $\cos^2 \theta + \sin^2 \theta = 1$, the expression simplifies to $\sin \theta \cos \theta$, which is $\frac{1}{2} \sin(2\theta)$ by the double angle formula for sine.

Choose the One Alternative That Best Completes the Statement or Answers