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) $uv = π^{4} /16$ .

What is the complete set of a for which (1) has a real solution?

Answer:

Solution:

Since $0 \leq u \leq π$ and $0 \leq v \leq π^{2} /4$ independently, $0 \leq u + v \leq π + π^{2} /4$ . Hence $0 \leq a \leq 1 + 4/ π$ .

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

⏱ 2mℹ️ Source: QB

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