The double–angle expression for cosine is

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

Problem

The double–angle expression for cosine is cos⁡2x=cos⁡2x−sin⁡2x\cos 2x = \cos^{2}x - \sin^{2}x. Answer the following questions related to this identity. (i) Rewrite cos⁡2x\cos 2x entirely in terms of sin⁡x\sin x only. (ii) Rewrite cos⁡2x\cos 2x entirely in terms of cos⁡x\cos x only. (iii) Explain, with reference to the Pythagorean identity, why the two alternate forms obtained in parts (i) and (ii) are equal for every real value of xx."

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