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

Let $u = cos^{- 1} x$ and $v = (sin^{- 1} y)^{2}$ , where $x, y \in [- 1, 1]$ . Equations (1) $u + v = a π^{2} /4$ and (2) $uv = π^{4} /16$ .

Which a allow simultaneous solutions of (1) and (2)?

Options:

Answer:

Solution:

With $uv = π^{4} /16$ , both u and v are positive. Their common value at the minimum sum is $π^{2} /4$ , giving $a = 2$ . For fixed product, the sum increases to its maximum at $u = π, v = π^{3} /16$ , yielding $a = 4/ π + π /4$ . Exact a interval: $[2, 4/ π + π /4]$ , which is option C.

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

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...