If sin-1 x - -5 for some x - -1-1- then the value of cos-1x is-IIT 1992-

Sin^ 1 x + cos^ 1 x = π/2 ⇒ cos^ 1 x = π/2 sin^ 1 x = π/2 π/5 = 3π/10. ...

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Trigonometric Identities

If sin-1 x = ...

Question

If $s i n^{- 1} x = \frac{π}{5}$ for some $x ϵ (- 1, 1),$ then the value of $c o s^{- 1} x$ is
[IIT 1992]

$\frac{3 π}{10}$

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$\frac{5 π}{10}$

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$\frac{7 π}{10}$

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$\frac{9 π}{10}$

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If $s i n^{- 1} x = \frac{π}{5}$ for some $x ϵ (- 1, 1),$ then the value of $c o s^{- 1} x$ is
[IIT 1992]

{sin}^{- 1} x = \frac{π}{5}

x \in [- 1, 1]

{cos}^{- 1} x .

\frac{π}{5}

{sin}^{- 1} x = \frac{π}{5}

x \in (- 1, 1)

{cos}^{- 1} x

{sin}^{- 1} x = \frac{π}{5} x \in [- 1, 1]

{cos}^{- 1} x

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