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The value of "tan"(sin^(-1)("cos"(sin^(-...

The value of `"tan"(sin^(-1)("cos"(sin^(-1)x)))"tan"(cos^(-1)(sin(cos^(-1)x))),w h e r ex in (0,1),` is equal to (a) 0 (b) 1 (c) `-1` (d) none of these

A

0

B

1

C

`-1`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`tan (sin^(-1) (cos (sin^(-1) x))) tan(cos^(-1) (sin (cos^(-1) x)))`
`= tan(sin^(-1) (cos (cos^(-1) sqrt(1 -x^(2)))))`
`tan {cos^(-1) (sin (sin^(-1) sqrt(1 -x^(2))))}`
`= tan (sin^(-1) sqrt(1 -x^(2)) tan (cos^(-1) sqrt(1 - x^(2)))`
`= tan (cos^(-1) x) tan (sin^(-1) x)`
`= tan(cos^(-1) x) tan (pi//2 - cos^(-1 x)`
`= tan (cos^(-1) x) cot (cos^(-1) x) = 1`
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CENGAGE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
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