Inverse Trig Squared Sum Maximum (Jee Mains)

Principal Value & Basic Properties

Medium

Inverse Trig Squared Sum Maximum

Let the maximum value of (sin^–1x)² + (cos^–1x)² for x∈ $\left[ { - \frac{{\sqrt 3 }}{2},\frac{1}{{\sqrt 2 }}} \right]$ be $\frac{m}{n}{\pi ^2}$ , where gcd (m, n) = 1.
Then m + n is equal to _______.

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