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For x in(0,1), let alpha=sin^(-1)x,beta=...

For `x in(0,1)`, let `alpha=sin^(-1)x,beta=x,gamma=tan^(-1)x, delta=cot^(-1)x-(pi)/(2)`. Which of the following is true ?

A

`alpha gt beta gt gamma`

B

`beta gt alpha gt gamma gt delta`

C

`alpha gt beta gt gamma gt delta`

D

`beta gt alpha gt delta gt gamma`

Text Solution

Verified by Experts

The correct Answer is:
C
For `x in (0,1)`
`sin^(-1)x gt x gt tan^(-1)x gt cot^(-1)x-(pi)/(2)`
as `cot^(-1)x-(pi)/(2)=-(tan^(-1)x)`
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