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

Question

10397 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-18T19:04:09

We know that

$cos2x=cos^2x-sin^2x=1-2sin^2x$

Hence

$sin^2x=1/2*(1-cos2x)$

Set $x->t/2$ so we have

$sin^2(t/2)=1/2*(1-cost)$

Multiply and divide the LHS with $1+cost$ hence

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

Which proves the requested

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