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Question: If minimum value of (sin<sup>–1</sup> x)<sup>2</sup> + (cos<sup>–1</sup> x)<sup>2</sup> is \(\frac{\...

If minimum value of (sin–1 x)2 + (cos–1 x)2 is π2k\frac{\pi^{2}}{k}, then the value of k is

A

(a) 4

B

6

C

8

D

None of these

Answer

8

Explanation

Solution

(sin–1 x)2 + (π2−sin⁡−1x)2\left( \frac{\pi}{2} - \sin^{- 1}x \right)^{2}

= 2(sin–1 x)2 – p sin–1 x + π24\frac{\pi^{2}}{4}

so minimum value is that expression is π28\frac{\pi^{2}}{8}

so, k = 8