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The solution of sin^(-1)xlecos^(-1)x i...

The solution of `sin^(-1)xlecos^(-1)x` is

A

`(-1,(1)/(sqrt(2)))`

B

`[-1,(1)/(sqrt(2))]`

C

`[1,(1)/(sqrt(2))]`

D

`(1,(1)/(sqrt(2)))`

Text Solution

Verified by Experts

The correct Answer is:
B
Given , `cos^(-1)xgesin^(-1)x`
`rArr(pi)/(2)ge2sin^(-1)x[becausesin^(-1)x+cos^(-1)x=(pi)/(2)AAx in(-1,1)]`
`rArrsin^(-1)xle(pi)/(4)rArr-1lexlesin((pi)/(4))rArrx in[-1,(1)/(sqrt(2))]`
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