Expert answers to "How to prove that sin2(x2)=sin2x2(1+cos⁡x)?"

gibbokf5

Answered question

2022-12-25

How to prove that

\sin^{2} (\frac{x}{2}) = \frac{\sin^{2} x}{2 (1 + \cos x)}

wolfnightswimfdi

Beginner2022-12-26Added 9 answers

We know

\cos 2 x = \cos^{2} x - \sin^{2} x = 1 - 2 \sin^{2} x

Hence

\sin^{2} x = \frac{1}{2} \cdot (1 - \cos 2 x)

Set

x \to \frac{t}{2}

so we have

\sin^{2} (\frac{t}{2}) = \frac{1}{2} \cdot (1 - \cos t)

Divide and multiply the LHS with

1 + \cos t

hence
PSKsin^2(t/2)=1/2*[((1-cost)*(1+cost))/(1+cost)]=>
sin^2(t/2)=1/2*[(1-cos^2t)/(1+cost)]=>
sin^2(t/2)=1/2*[sin^2t/(1+cost)]ZSK

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