MathsJEE Main 22 Jan 2026, Shift 2·Q23·Numerical·Moderate

Trigonometry · Compound angle formulae

Let

\cos(\alpha + \beta) = -\dfrac{1}{10}

and

\sin(\alpha - \beta) = \dfrac38

, where

0 < \alpha < \dfrac{\pi}{3}

and

0 < \beta < \dfrac{\pi}{4}

. If

\tan2\alpha = \dfrac{3\left(1 - r\sqrt5\right)}{\sqrt{11}\left(s + \sqrt5\right)}

r, s \in \mathbb{N}

, then

r + s

is equal to .

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