NVAMediumJEE Main 2026 · 22 January, Shift 2Trigonometric Equations

Mathematics Question from JEE Main 2026 · 22 January, Shift 2

Let cos⁡(α+β)=−110\cos(\alpha + \beta) = -\dfrac{1}{10} and sin⁡(α−β)=38\sin(\alpha - \beta) = \dfrac{3}{8}, where 0<α<π30 < \alpha < \dfrac{\pi}{3} and 0<β<π40 < \beta < \dfrac{\pi}{4}.

If tan⁡2α=3(1−r5)11(s+5),r,s∈N\tan 2\alpha = \frac{3(1 - r\sqrt{5})}{\sqrt{11}(s + \sqrt{5})}, \quad r, s \in \mathbb{N}, then the value of r+sr + s is _____.

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