If $\sin ^{-1} \frac{\alpha}{17}+\cos ^{-1} \frac{4}{5}-\tan ^{-1} \frac{77}{36}=0,0<\alpha<13$, then $\sin ^{-1}(\sin \alpha)+\cos ^{-1}(\cos \alpha)$ is equal to

JEE Main · 2023 · 31 Jan 2023 · Shift 1 · Inverse Trigonometric Functions

sin^{- 1} \frac{α}{17} + cos^{- 1} \frac{4}{5} - tan^{- 1} \frac{77}{36} = 0, 0 < α < 13

, then

sin^{- 1} (sin α) + cos^{- 1} (cos α)

is equal to

Answer: (A)

Since

cos^{- 1} \frac{4}{5} = tan^{- 1} \frac{3}{4}

, the given relation becomes

sin^{- 1} \frac{α}{17} = tan^{- 1} \frac{77}{36} - tan^{- 1} \frac{3}{4} = tan^{- 1} \frac{8}{15} = sin^{- 1} \frac{8}{17}

, so

α = 8

. For

8

radians, which lies in

(\frac{5 π}{2}, 3 π)

sin^{- 1} (sin 8) = 3 π - 8

and

cos^{- 1} (cos 8) = 8 - 2 π

. Adding these,

sin^{- 1} (sin 8) + cos^{- 1} (cos 8) = π

JEE Main · 2023 · 31 Jan 2023 · Shift 1 · Single correct option

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