If sin − 1 ( sin ( 1 + x 2 2 x 2 + 4 ) ) < π − 3 then x satisfies

sin − 1 ( sin ( π − ( 2 + 1 + x 2 2 ) ) ) < π − 3 ⇒ π − 2 − 1 + x 2 2 < π − 3 ⇒ ∣ x ∣ < 1

Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

MathematicsInverse Trigonometric FunctionsIdentities, eqations and inequations involving ITFMedium2 minQB

MathematicsMediumsingle choice

If $sin^{- 1} (sin (\frac{2 x ^{2} + 4}{1 + x ^{2}})) < π - 3$ then $x$ satisfies

Answer:

Solution:

$sin^{- 1} (sin (π - (2 + \frac{2}{1 + x ^{2}}))) < π - 3 \Rightarrow π - 2 - \frac{2}{1 + x ^{2}} < π - 3$

$\Rightarrow ∣ x ∣ < 1$

Stream:JEESubject:MathematicsTopic:Inverse Trigonometric FunctionsSubtopic:Identities, eqations and inequations involving ITF

⏱ 2mℹ️ Source: QB

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