Start Free Mock LoginAlready registered? Login here

Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

MathematicsInverse Trigonometric FunctionsIdentities, eqations and inequations involving ITFMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

Use principal branches of $tan^{- 1}, sin^{- 1}$ and $cos^{- 1}$ . For $x > 1$ , $tan^{- 1} (2 x / (1 - x^{2})) = 2 tan^{- 1} x - π$ ; for $∣ x ∣ \leq 1, sin^{- 1} (2 x / (1 + x^{2})) = 2 tan^{- 1} x$ . Also $sin^{- 1} u + cos^{- 1} u = π /2$ on $[- 1, 1]$ .

Which listed interval is the full maximal interval on which $sin^{- 1} (4 x / (x^{2} + 4)) + 2 tan^{- 1} (- x /2)$ is constant?

Options:

Answer:

Solution:

Write $z = x /2$ . The expression is $sin^{- 1} (2 z / (1 + z^{2})) - 2 tan^{- 1} z$ . On $∣ z ∣ \leq 1$ it equals zero throughout $[- 2, 2]$ . Outside that interval the principal branch changes and the expression is not constant over the entire listed interval.

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

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...