Question

Find the positive expression for sin⁡(a/2) in terms of cos⁡(a).

Answer 1

Hi ,

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Cos 2A = cos² A - sin² A

= 1 - sin² A - sin² A

Cos 2A = 1 - 2sin²A

2sin²A = 1 - cos 2A

sin² A = ( 1 - cos2A )/2

sinA = √ ( 1 - cos2A )/2

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Now ,

Sin A/2 = √ [( 1 - cos A )/2 ]

I hope this helps you.

: )