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Question: The value of x for which cos<sup>–1</sup> (cos 4) \> 3x<sup>2</sup> – 4x, is –...

The value of x for which cos–1 (cos 4) > 3x2 – 4x, is –

A

(0,2+6π−83)\left( 0 , \frac { 2 + \sqrt { 6 \pi - 8 } } { 3 } \right)

B

(2−6π−83,0)\left( \frac { 2 - \sqrt { 6 \pi - 8 } } { 3 } , 0 \right)

C

(–2, 2)

D

(2−6π−83,2+6π−83)\left( \frac { 2 - \sqrt { 6 \pi - 8 } } { 3 } , \frac { 2 + \sqrt { 6 \pi - 8 } } { 3 } \right)

Answer

(2−6π−83,2+6π−83)\left( \frac { 2 - \sqrt { 6 \pi - 8 } } { 3 } , \frac { 2 + \sqrt { 6 \pi - 8 } } { 3 } \right)

Explanation

Solution

cos–1(cos 4) = cos–1 {cos (2p – 4)} = 2p – 4

\ cos–1 (cos 4) > 3x2 – 4x

Ž 2p – 4 > 3x2 – 4x

Ž 3x2 – 4x – (2p – 4) < 0

Ž 2−6π−83<x<2+6π−83\frac { 2 - \sqrt { 6 \pi - 8 } } { 3 } < x < \frac { 2 + \sqrt { 6 \pi - 8 } } { 3 }