The complete solution set of the inequality (cos)- 1 (. cos 4 .) 3 x2 - 4 x is

Question

The complete solution set of the inequality (cos)- 1 (. cos 4 .) > 3 x2 - 4 x is (A) (0 , (2 + √6 π - 8/3)) (B) ((2 - √6 π - 8/3) , 0) (C) (.-2, 2.) (D) ((2 - √6 π - 8/3) , (2 + √6 π - 8/3))

Tardigrade Admin · Accepted Answer

As, (cos)- 1 (. cos â¡ 4 .) = (cos)- 1 â¡ cos â¡ (2 π - 4) = 2 π - 4 â 2π -4>3x2-4x â 3x2-4x-(2 π - 4) < 0 â (2 - √6 π - 8/3) < x < (2 + √6 π - 8/3)

Q. The complete solution set of the inequality $(cos)^{- 1} (cos 4) > 3 x^{2} - 4 x$ is

$(0, \frac{2 + 6 π - 8}{3})$

$(\frac{2 - 6 π - 8}{3}, 0)$

$(- 2, 2)$

$(\frac{2 - 6 π - 8}{3}, \frac{2 + 6 π - 8}{3})$

As, $(cos)^{- 1} (cos 4) = (cos)^{- 1} {cos (2 π - 4)} = 2 π - 4$
$\Rightarrow 2 π - 4 > 3 x^{2} - 4 x$
$\Rightarrow 3 x^{2} - 4 x - (2 π - 4) < 0$
$\Rightarrow \frac{2 - 6 π - 8}{3} < x < \frac{2 + 6 π - 8}{3}$

Q. The complete solution set of the inequality (cos)−1(cos4)>3x2−4x is

(0,32+6π−8​​)

(32−6π−8​​,0)

(−2,2)

(32−6π−8​​,32+6π−8​​)