If . Then, prove that…

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

If {sin⁡(α−β)+cos⁡(α+2β)sin⁡β}2=4cos⁡αsin⁡βsin⁡(α+β)\{\sin(\alpha - \beta) + \cos(\alpha + 2\beta)\sin\beta\}^2 = 4 \cos \alpha \sin \beta \sin(\alpha + \beta) . Then, prove that tan⁡α+tan⁡β=tan⁡β(2cos⁡β−1)2;\tan \alpha + \tan \beta = \frac{\tan \beta}{(\sqrt{2} \cos \beta - 1)^2}; α,β∈(0,π/4)\alpha, \beta \in (0, \pi/4) .

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