Prove the following trigonometric identity for .

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Prove the following trigonometric identity for 0∘<θ<90∘0^\circ<\theta<90^\circ. (i) Show that (1−sin⁡θ)(1+sin⁡θ)=cos⁡2θ(1-\sin\theta)(1+\sin\theta)=\cos^2\theta. (ii) After proving the identity, verify it numerically for θ=60∘\theta=60^\circ."

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