If sin − 1 ( 5 x ) + cosec − 1 ( 4 5 ) = 2 π then a value of x is

sin − 1 5 x + sin − 1 5 4 = 2 π ⇒ sin − 1 5 x = cos − 1 5 4 ⇒ sin − 1 5 x = sin − 1 5 3 ∴ x = 3 .

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Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

MathematicsInverse Trigonometric FunctionsGeneral ( General, Domain, Range & Graph)Easy2 minPYQ_2007

MathematicsEasysingle choice

If $sin^{- 1} (\frac{x}{5}) + cosec^{- 1} (\frac{5}{4}) = \frac{π}{2}$ then a value of $x$ is

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Solution:

$sin^{- 1} \frac{x}{5} + sin^{- 1} \frac{4}{5} = \frac{π}{2}$ $\Rightarrow sin^{- 1} \frac{x}{5} = cos^{- 1} \frac{4}{5} \Rightarrow sin^{- 1} \frac{x}{5} = sin^{- 1} \frac{3}{5}$ $∴ x = 3$ .

Stream:JEESubject:MathematicsTopic:Inverse Trigonometric FunctionsSubtopic:General ( General, Domain, Range & Graph)

⏱ 2mℹ️ Source: PYQ_2007

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