Let be an angle for which all the expressions involved are defined.

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

Problem

Let θ\theta be an angle for which all the expressions involved are defined. (i) Show that 1−cos⁡2θ=2sin⁡2θ1-\cos 2\theta = 2\sin^{2}\theta. (ii) Hence verify that 1−cos⁡2θsin⁡θcos⁡θ=2tan⁡θ.\frac{1-\cos 2\theta}{\sin\theta\cos\theta}=2\tan\theta.

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