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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) $uv = π^{4} /16$ .

For an integral value of a, which ordered pairs (x,y) solve both equations?

Options:

Answer:

Solution:

The simultaneous-solution interval $[2, 4/ π + π /4]$ has only the integer $a = 2$ . Equality in $u + v \geq 2 uv$ forces $u = v = π^{2} /4$ . Thus $x = cos (π^{2} /4), (sin^{- 1} y)^{2} = π^{2} /4$ , and $y = \pm 1$ .

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

⏱ 2mℹ️ Source: QB

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