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The range of the values of p for which t...

The range of the values of p for which the equation ` sin cos^(-1) ( cos (tan^(-1) x)) = p` has a solution is

A

`(-(1)/(sqrt2), (1)/(sqrt2))`

B

`[0, 1)`

C

`((1)/(sqrt2), 1)`

D

`(-1, 1)`

Text Solution

Verified by Experts

The correct Answer is:
B
`sin cos^(-1) (cos (tan^(-1) x)) = p`
For `x in R, tan^(-1) x in (-pi//2, pi//2)`, we have
`cos (tan^(-1) x) in (0, 1]`
`sin (cos^(-1) (cos (tan^(-1) x))) in [0,1)`
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