Question

Sin^-1(sin5) > x^2 -4x if x=?​

Answer 1

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xε(2−9−2π,2+9−2π ) is the answer

Since 3π/2<5<2π, we have sin 5 < 0, so sin−1(sin5)=5−2π. Therefore, the given inequality can be written as 5−2π>x2−4x or x2−4x+(2π−5)<0

So -

⇒[x−24−16−4(2π−5)][x−216−4(2π−5)]<0

⇒[x−(2−9−2π)][x−(2+9−2π)]<0

⇒xε(2−9−2π,2+9−2π)

HOPE IT HELPS YOU