Asked by julia
2*cos^2(a/2)=(sin^2(a))/(1-cos(a))
can anyone help to prove this identity?
can anyone help to prove this identity?
Answers
Answered by
drwls
First note that sin^2 a = 1 - cos^2a
= (1+cos a)(1-cosa)
That means you can cancel out the denominator on the right side after which it becomes (1 + cos a)
On the left side, use the half angle formula:
cos (a/2) = sqrt[(1/2)(1 + cos a)]
which I will not prove. That leads to
cos^2(a/2) = (1/2)(1 + cos a)
2 cos^2(a/2) = 1 + cos a
= (1+cos a)(1-cosa)
That means you can cancel out the denominator on the right side after which it becomes (1 + cos a)
On the left side, use the half angle formula:
cos (a/2) = sqrt[(1/2)(1 + cos a)]
which I will not prove. That leads to
cos^2(a/2) = (1/2)(1 + cos a)
2 cos^2(a/2) = 1 + cos a
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