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  4. If sin -1(x2-7 x+12)=n π, ∀ n ∈ I, then x=

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Q. If $\sin ^{-1}\left(x^{2}-7 x+12\right)=n \pi, \forall n \in I$, then $x=$

Inverse Trigonometric Functions

Solution:

$\sin ^{-1}\left(x^{2}-7 x+12\right)=n \pi $
$\Rightarrow x^{2}-7 x+12=\sin n \pi$
$\Rightarrow x^{2}-7 x+12=0\,\,\,\,\,$$(\because \sin n \pi=0 \forall n \in I )$
$\Rightarrow (x-4)(x-3)=0 $
$\Rightarrow x=4,3$