Mathematics

Mathematics

Problem

Let θ\theta be any angle for which tan⁡θ\tan\theta is defined and let t=tan⁡θt=\tan\theta. (i) Express sin⁡θ\sin\theta solely in terms of tt. (ii) Express cos⁡θ\cos\theta solely in terms of tt. (iii) Using the above results, prove that 1+tan⁡2θ=1cos⁡2θ1+\tan^2\theta = \dfrac{1}{\cos^2\theta}.

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