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 ?

Options

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`

Answer

C

Explanation

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)`