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Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

MathematicsInverse Trigonometric FunctionsIdentities, eqations and inequations involving ITFMedium2 minQB

MathematicsMediumsingle choice

If $sin^{- 1} (a - a^{2} /3 + a^{3} /9 - \dots) + cos^{- 1} (1 + b + b^{2} + \dots) = π /2$ , which listed pair can work? Assume both series converge and inverse arguments are real.

Options:

Answer:

Solution:

The arguments must equal: a/(1+a/3)=1/(1-b). For a=1,b=-1/3 both sides are 3/4 and the series converge. Other listed pairs fail the equality or convergence. The equation may have other solutions outside these choices.

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

⏱ 2mℹ️ Source: QB

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