Let and , where . Then, is equal…

MATHEMATICS · Single correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Let cos⁡(α+β)=45\cos(\alpha + \beta) = \frac{4}{5} and sin⁡(α−β)=513\sin(\alpha - \beta) = \frac{5}{13} , where 0≤α,β≤π40 \le \alpha, \beta \le \frac{\pi}{4} . Then, tan⁡2α\tan 2\alpha is equal to (1) 2516\frac{25}{16} (2) 5633\frac{56}{33} (3) 1912\frac{19}{12} (4) 207\frac{20}{7}

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