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MathsJEE Main 6 Apr 2026, Shift 1·Q24·Numerical·Moderate

Trigonometry · Extreme values of trigonometric functions

For the functions f(θ)=αtan⁡2θ+βcot⁡2θf(\theta) = \alpha\tan^2\theta + \beta\cot^2\theta, and g(θ)=αsin⁡2θ+βcos⁡2θg(\theta) = \alpha\sin^2\theta + \beta\cos^2\theta, α>β>0\alpha > \beta > 0, let min⁡0<θ<π2f(θ)=max⁡0<θ<πg(θ)\displaystyle\min_{0<\theta<\frac{\pi}{2}} f(\theta) = \max_{0<\theta<\pi} g(\theta). If the first term of a G.P. is (α2β)\left(\dfrac{\alpha}{2\beta}\right), its common ratio is (2βα)\left(\dfrac{2\beta}{\alpha}\right) and the sum of its first 10 terms is mn\dfrac{m}{n}, gcd⁡(m,n)=1\gcd(m, n) = 1, then m+nm + n is equal to .

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