The value of cos ( 2 cos − 1 x + sin − 1 x ) at x = 5 1 is

cos [ 2 cos − 1 x + sin − 1 x ] = cos [ cos − 1 x + cos − 1 x + sin − 1 x ] = cos [ cos − 1 x + 2 π ] = − sin [ cos − 1 x ] = − sin [ sin − 1 1 − x 2 ] = − 1 − x 2 = − 1 − ( 5 1 ) 2 = − 25 24 = − 5 2 6

Mathematics - Inverse Trigonometric Function Question with Solution | TestHub

MathematicsInverse Trigonometric FunctionIdentities, eqations and inequations involving ITFMedium2 minPYQ_2021

MathematicsMediumsingle choice

The value of $cos (2 cos^{- 1} x + sin^{- 1} x)$ at $x = \frac{1}{5}$ is

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Answer:

Solution:

$cos [2 cos^{- 1} x + sin^{- 1} x]$ $= cos [cos^{- 1} x + cos^{- 1} x + sin^{- 1} x]$ $= cos [cos^{- 1} x + \frac{π}{2}] = - sin [cos^{- 1} x]$ $= - sin [sin^{- 1} 1 - x^{2}] = - 1 - x^{2}$ $= - 1 - (\frac{1}{5})^{2} = - \frac{24}{25} = - \frac{2 6}{5}$

Stream:BITSATSubject:MathematicsTopic:Inverse Trigonometric FunctionSubtopic:Identities, eqations and inequations involving ITF

⏱ 2mℹ️ Source: PYQ_2021

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