Assertion (A) : $\cos^{- 1} x \geq \sin^{- 1} x, \forall x \in [- 1, 1]$
Reason (R) : $\cos^{- 1} x$ is decreasing functions $\forall x \in [- 1, 1]$

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Both A and R are true and R is the correct explanation of A

A is false but R is true

Both A and R are true but R is not correct explanation of A

A is true but R is false

answer is D.

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Detailed Solution

$(A) \frac{π}{2} - \sin^{- 1} \geq \sin^{- 1} x \Rightarrow \frac{π}{2} \geq 2 \sin^{- 1} x \Rightarrow \sin^{- 1} x \leq \frac{π}{4} \Rightarrow x \leq \frac{1}{\sqrt{2}}$

$(R) \cos^{- 1} x$ always decreasing functions.

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