Verify this is an identity? 2 sin^2 (u/2)=sin^2u/(1+cosu)

2 Answers
Apr 3, 2018

LHS=2 sin^2 (u/2)

=(2 sin^2 (u/2)xx2cos^2(u/2))/(2cos^2(u/2))

=(2 sin (u/2)cos(u/2))^2/(1+cosu)

=sin^2u/(1+cosu)=RHS

Apr 3, 2018

Proof

Explanation:

Let us start with LHS.

=2sin^2(u/2)

=(2sin^2(u/2) \times 2cos^2(u/2))/(2cos^2(u/2))

=(2sin(u/2)cos(u/2))^2/(2cos^2(u/2))

sin(2 theta) = 2sintheta cos theta and cos (2 theta) = 2cos^2theta - 1. So,

=sin^2u/(1+cos u)

You can prove the same starting from RHS too.....