If , and , then find the value of…

MATHEMATICS · Subjective · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

If cos⁡(α+β)=45\cos(\alpha + \beta) = \frac{4}{5} , sin⁡(α−β)=513\sin(\alpha - \beta) = \frac{5}{13} and α,β∈(0,π4)\alpha, \beta \in \left(0, \frac{\pi}{4}\right) , then find the value of tan⁡2α\tan 2\alpha .

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