How do you prove that $sin^2(x/2) = (1-cos^2x)/(2(1+cosx))$ ?

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Answer 1 · 2016-01-09T14:48:16

This is not a valid identity.

Working only with the right hand side:

$(1-cos^2x)/(2(1+cosx))$

Use the Pythagorean Identity in the numerator.

$=sin^2x/(2(1+cosx))$

Split apart the fraction.

$=(sinx/2)(sinx/(1+cosx))$

Use the tangent half angle identity.

$=1/2sinxtan(x/2)$

There is nothing you could do here to make this equal $sin^2(x/2)$ .

How do you prove that sin^2(x/2) = (1-cos^2x)/(2(1+cosx)) sin^2(x/2) = (1-cos^2x)/(2(1+cosx)) ?