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Chapter 7: Q. 2 (page 495)

$\sin^{2} \frac{θ}{2} = \frac{______}{2}$ .

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given Data

The given incomplete equation is

$\sin^{2} \frac{θ}{2} = \frac{______}{2}$

02

Step 2. Explanation

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

Substitute $\frac{θ}{2}$ for $θ$

localid="1646428514535" $\sin^{2} θ = \frac{1 - \cos (2 θ)}{2} \sin^{2} \frac{θ}{2} = \frac{1 - \cos (2 \times \frac{θ}{2})}{2} \sin^{2} \frac{θ}{2} = \frac{1 - \cos (θ)}{2}$

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