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If cos(alpha+beta)=(4)/(5) and sin(alpha...

If `cos(alpha+beta)=(4)/(5) and sin(alpha-beta)=(5)/(13)` , where `alpha` lie between 0 and ` (pi)/(4)`, then find that value of `tan2alpha`.

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To find the value of \( \tan 2\alpha \) given \( \cos(\alpha + \beta) = \frac{4}{5} \) and \( \sin(\alpha - \beta) = \frac{5}{13} \), we will follow these steps: ### Step 1: Find \( \sin(\alpha + \beta) \) We know that: \[ \sin(\alpha + \beta) = \sqrt{1 - \cos^2(\alpha + \beta)} \] Substituting the value of \( \cos(\alpha + \beta) \): ...
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