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

Question

Quizplus · Accepted Answer

This identity can be derived from the double angle formula for sine, which states that $\sin(2x) = 2\sin(x)\cos(x)$. By substituting $\frac{\theta}{2}$ for $x$, we get $\sin(\theta) = 2\sin(\frac{\theta}{2})\cos(\frac{\theta}{2})$. Rearranging this equation gives $\sin(\frac{\theta}{2})\cos(\frac{\theta}{2}) = \frac{1}{2}\sin(\theta)$, which matches choice A.

Choose the One Alternative That Best Completes the Statement or Answers