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If f(x)=sin^(-1)(sin x),g(x)=cos^(-1)(co...

If `f(x)=sin^(-1)(sin x),g(x)=cos^(-1)(cos x)` and `h(x)=cot^(-1)(cot x)`, then which of the following is/are correct ?

A

`f(x)=g(x)=h(x)AA x in((pi)/(4),(pi)/(3))`

B

`f(x)lt g(x)lt h(x)AA x in ((pi)/(2),pi)`

C

`h(x)gt g(x)gt f(x)AA x in((3pi)/(2),2pi)`

D

`f(x)gt g(x)` has no real solution

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
First draw the graph of y = f(x), y = g(x) and y = h(x) for `x in [0, 2pi]`

From the graphs, we can see that options (a), (c ) and (d) are correct.
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