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The simplest form of (cos^(-1)x +cos^(-1...

The simplest form of `(cos^(-1)x +cos^(-1){x/2+1/2sqrt(3-3x^2)}),AA x in [1/2,1]` is A. Then the value of tanA is

A

`1sqrt3`

B

`sqrt3`

C

1

D

-1

Text Solution

Verified by Experts

The correct Answer is:
B
Given,
`A=cos^(-1)x+cos^(-1){x/2+sqrt3/2sqrt(1-x^2)}`
`=cos^(-1)x+cos^(-1){1/2x+sqrt(1-1/4)sqrt(1-x^2)}`
`=cos^(-1)x+cos^(-1)1/2-cos^(-1)x`
`cos^(-1)1/2`
`=pi/3`
`rArr tanA=tan.pi/3=sqrt3`
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