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The range of value of p for which the eq...

The range of value of `p` for which the equation `sincos^(-1)("cos"(tan^(-1)x))=p` has a solution is `(-1/(sqrt(2)),1/(sqrt(2))` (b) (0,1) `(1/(sqrt(2)),1)` (d) `(-1,1)`

A

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

B

B. `[0, 1)`

C

C. `((1)/(sqrt2), 1)`

D

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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