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Let -1<=x<=1 If cos(sin^(-1) x)=1/2, the...

Let `-1<=x<=1` If `cos(sin^(-1) x)=1/2`, then how many value does `tan(cos^(-1)x)` assume?

A

One

B

Two

C

Four

D

Infinite

Text Solution

Verified by Experts

The correct Answer is:
B
As given :
`cos(sin^(-1)x)=(1)/(2)`
`rArr sin^(-1)x = cos^(-1)((1)/(2))`
`rArr sin^(-1)x=(pi)/(3) rArr x = "sin"(pi)/(3)=(sqrt(3))/(2)`
`therefore tan(cos^(-1)x)=tan("cos"^(-1)(sqrt(3))/(2))`
`=tan(+-(pi)/(6))=+-(1)/(sqrt(3))`
Hence, tan `(cos^(-1)x)` have two values.
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