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Prove the following:

    2. 3\cos^{-1} x = \cos^{-1}(4x^3 - 3x), \;\;x\in\left[\frac{1}{2},1 \right ]

Given to prove . Take   or ; Then we have; R.H.S. =        =  =  =  = L.H.S Hence Proved.

Prove the following:

    1. 3\sin^{-1}x = \sin^{-1}(3x - 4x^3),\;\;x\in\left[-\frac{1}{2},\frac{1}{2} \right ]

Given to prove:       where,     . Take   or   Take R.H.S value   =  =                                         =  =    =   L.H.S
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