Which of the following is true? Inverse Trigonometric Functions

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Solution

Q.
Which of the following is true

1 $\frac{d y}{d x} for y = \sin^{- 1} (\cos x), where x \in (0, π), is - 1$

2 $\frac{d y}{d x} for y = \sin^{- 1} (\cos x), where x \in (0, 2 π), is 1$

3 $\frac{d y}{d x} for y = \cos^{- 1} (\sin x), where x \in (- π, \frac{π}{2}), is - 1$

4 $\frac{d y}{d x} for y = \cos^{- 1} (\sin x), where x \in (- \frac{π}{2}, \frac{3 π}{2}), is - 1$

Ans.
(1)

$Use graphs of \sin^{- 1} (\sin x) and \cos^{- 1} (\cos x)$

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