Complete the identity.
-$\sin ^ { 2 } \frac { \theta } { 2 } = ?$
A) $\frac { \sec \theta - 1 } { 2 \sec \theta }$
B) $\frac { \sec \theta + 1 } { 2 \sec \theta }$
C) $\frac { - \sec \theta - 1 } { 2 \sec \theta }$
D) $\frac { - \sec \theta + 1 } { 2 \sec \theta }$

Question

Quizplus · Accepted Answer

The correct identity is derived from the half-angle formula for sine, which is $\sin^2\frac{\theta}{2} = \frac{1 - \cos\theta}{2}$. Since $\sec\theta = \frac{1}{\cos\theta}$, rearranging gives $\sin^2\frac{\theta}{2} = \frac{1 - \frac{1}{\sec\theta}}{2} = \frac{\sec\theta - 1}{2\sec\theta}$.

Complete the Identity sin⁡2θ2=?\sin ^ { 2 } \frac { \theta } { 2 } = ?sin22θ​=?

Complete the Identity $\sin ^ { 2 } \frac { \theta } { 2 } = ?$