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

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Answer 1 · 2018-04-03T04:17:52

#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#

Answer 2 · 2018-04-03T04:20:36

Proof

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.....