Question

${\sin }^2\frac{\theta }{2}=\frac{\_\_\_\_\_\_}{2}$.

Short answer

${\sin }^2\frac{\theta }{2}=\frac{\underset{⏝}{1-\cos \left(\theta \right)}}{2}$.

Step-by-step solution

Step 1. Given Data 

The given incomplete equation is

${\sin }^2\frac{\theta }{2}=\frac{\_\_\_\_\_\_}{2}$

Step 2. Explanation 

as known${\sin }^2\theta =\frac{1-\cos \left(2\theta \right)}{2}$

Substitute $\frac{\theta }{2}$for$\theta$

localid="1646428514535" $$\begin{gathered} {\sin }^2\theta =\frac{1-\cos \left(2\theta \right)}{2} \\ {\sin }^2\frac{\theta }{2}=\frac{1-\cos \left(2\times {\displaystyle \frac{\theta }{2}}\right)}{2} \\ {\sin }^2\frac{\theta }{2}=\frac{1-\cos \left(\theta \right)}{2} \end{gathered}$$