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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

we have
`cos(sin^(-1)x)=sqrt(1-x^(2)) and sin cos^(-1)x=sqrt(1-x^(2))`
`therefore tan{sin^(-1)(cos sin^(-1)x)}tan{cos^(-12)(sin(cos^(-1)x)}`
`=tan{sin^(-1)sqrt(1-x^(2))}tan{cos^(-1)sqrt(1-x^(2))`
`=tan(sin^(-1)sqrt(1-x^(2))tan{(pi)/(2)-sin^(-1)sqrt(1-x^(2))=1`
`=tan(sin^(-1)sqrt(1-x^(2))cot(sin^(-1))sqrt(1-x^(2))=1`
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OBJECTIVE RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTIONS -Section I - Solved Mcqs
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