The inequality sin -1( sin 5)x2-4 x holds if

Question

The inequality sin -1( sin 5)>x2-4 x holds if (A) x=2-√9-2π (B) x=2+√9-2π (C) x> 2+√9-2π (D) x ∈(2-√9-2π, 2+√9-2π)

Tardigrade Admin · Accepted Answer

(3 π/2)<5< (5 π/2) ⇒ textSin-1( textSin 5)=5-2 π Given sin -1( textSin 5) >x2-4 x ⇒ x2-4 x+4< 9-2 π ⇒ (x-2)2< 9-2 π ⇒ (x-2)2< 9-2 π ⇒ -√9-2 π < x-2 < √9-2 π ⇒ 2-√9-2 π < x < 2+√9-2 π

Q. The inequality $sin^{- 1} (sin 5) > x^{2} - 4 x$ holds if

$x = 2 - 9 - 2 π$

$x = 2 + 9 - 2 π$

$x > 2 + 9 - 2 π$

$x \in (2 - 9 - 2 π, 2 + 9 - 2 π)$

Q. The inequality sin−1(sin5)>x2−4x holds if

x=2−9−2π​

x=2+9−2π​

x>2+9−2π​

x∈(2−9−2π,​2+9−2π​)

23π​<5<25π​ ⇒Sin−1(Sin5)=5−2π Given sin−1(Sin5)>x2−4x ⇒x2−4x+4<9−2π ⇒(x−2)2<9−2π ⇒(x−2)2<9−2π ⇒−9−2π​<x−2<9−2π​ ⇒2−9−2π​<x<2+9−2π​

Q. The inequality $sin^{- 1} (sin 5) > x^{2} - 4 x$ holds if

$x = 2 - 9 - 2 π$

$x = 2 + 9 - 2 π$

$x > 2 + 9 - 2 π$

$x \in (2 - 9 - 2 π, 2 + 9 - 2 π)$