Mathematics - Inverse Trigonometric Function Question with Solution | TestHub

MathematicsInverse Trigonometric FunctionGeneral ( General, Domain, Range & Graph)Easy2 minPYQ_2024

MathematicsEasysingle choice

If $a = \sin^{- 1} (\sin (5))$ and $b = \cos^{- 1} (\cos (5))$ , then $a^{2} + b^{2}$ is equal to

Answer:

Solution:

Given: $a = \sin^{- 1} (\sin (5)) and b = \cos^{- 1} (\cos (5))$

$\Rightarrow a = 5 - 2 π and b = 2 π - 5$

$\Rightarrow a^{2} + b^{2} = {(5 - 2 π)}^{2} + {(2 π - 5)}^{2}$

$\Rightarrow a^{2} + b^{2} = 25 + 4 π^{2} - 20 π + 4 π^{2} + 25 - 20 π$

$\Rightarrow a^{2} + b^{2} = 8 π^{2} - 40 π + 50$

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

⏱ 2mℹ️ Source: PYQ_2024

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