(csc^2theta)/2=2/(1-costheta)

Question

Establishing an Identity, Double-angles and Half-angle Fourmula

Answer 1

cosθ = 1-2sin²(θ/2), double angle identity since θ = 2(θ/2).

Solve for sin²(θ/2),

sin²(θ/2) = (1/2)(1-cosθ)

Take reciprocal on both sides,

csc²(θ/2) = 2/(1-cosθ)

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Attn: You had a typo in the LHS. It should be csc^2(theta/2).