How can I prove trigonometric identities involving double-angle and half-angle formulas?

Answer 1

To prove trigonometric identities involving double-angle and half-angle formulas, use fundamental identities such as sin(2θ) = 2sin(θ)cos(θ) and cos(2θ) = cos²(θ) – sin²(θ). For half-angle formulas, use sin(θ/2) = ±√((1 – cos(θ))/2) and cos(θ/2) = ±√((1 + cos(θ))/2). Simplify expressions and verify both sides of the identity.

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