Sin -1sin 5-x2-4 x holds ifA- x-2-9-2 -B- -1-x-5- x -1 -5- -D- x -2-9-2 - 2-9-2 -

The correct option is D x ∈ (2 √(9 2 π),2+√(9 2 π))∴3π/2 lt; 5 lt; 5 π/2∴ sin^ 1(sin 5)=5 2π Given sin^ 1(sin 5) gt; x^2 4x ⇒ x^2 4x lt; 5 2 π ⇒ x^ ...

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Byju's Answer

Standard XII

Mathematics

Properties Derived from Trigonometric Identities

sin -1sin 5>x...

Question

$s i n^{- 1} (s i n 5) > x^{2} - 4 x$ holds if

x < 2 - \sqrt{9 - 2 π}

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- 1 < x < 5

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x \in (- \infty, - 1) \cup (5, \infty)

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x \in (2 - \sqrt{9 - 2 π}, 2 + \sqrt{9 - 2 π})

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Solution

The correct option is D $x \in (2 - \sqrt{9 - 2 π}, 2 + \sqrt{9 - 2 π})$
$∴ \frac{3 π}{2} < 5 < \frac{5 π}{2} ∴ s i n^{- 1} (s i n 5) = 5 - 2 π$
Given $s i n^{- 1} (s i n 5) > x^{2} - 4 x \Rightarrow x^{2} - 4 x < 5 - 2 π \Rightarrow x^{2} - 4 x + (2 π - 5) < 0 R o o t s o f x^{2} - 4 x + 2 π - 5 = 0 a r e 2 \pm \sqrt{9 - 2 π} ∴ x^{2} - 4 x + 2 π - 5 < 0 \Rightarrow 2 - \sqrt{9 - 2 π} < x < 2 + \sqrt{9 - 2 π}$

Suggest Corrections

sin−1(sin5)>x2−4x holds if

The correct option is D x∈(2−√9−2π,2+√9−2π)∴3π2<5<5π2∴sin−1(sin5)=5−2π Given sin−1(sin5)>x2−4x⇒x2−4x<5−2π⇒x2−4x+(2π−5)<0Roots of x2−4x+2π−5=0are2±√9−2π∴x2−4x+2π−5<0⇒2−√9−2π<x<2+√9−2π

$s i n^{- 1} (s i n 5) > x^{2} - 4 x$ holds if