IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

neeraj_agarwal_1990

greatest and least values of $({{sin}^{-1}x})^{3} +({{cos}^{-1}x})^{3}$ are ? i m able to convert it into $\frac{3\pi}{2}[({{sin}^{-1}x-\frac{\pi}{4}})^{2} +\frac{{\pi}^{2}}{12}-\frac{{\pi}^{2}}{16}]$
so minimum and maximum values should be at sin-1x =1 and -1 respectively....

joyfrancis

write cos^-1x as pi/2 - sin^-1x ..expand..and then differentiate to find critical pts..

neeraj_agarwal_1990

but wats wrong in what i did?

but answer is not matching!

hash_include

neeraj: minimum is when sin^-1x = pi/4 ..
maximum is when sin^-1x = - pi/2

neeraj_agarwal_1990

ya...got it...i did a very silly thing......took it as sinx!!!

joyfrancis

yea..min will not be at sin-1x = -1..woh maximum ho jaaygi ...

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