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tan(1/2cos^(- 1)\ sqrt(5)/3)...

`tan(1/2cos^(- 1)\ sqrt(5)/3)`

A

`(3-sqrt(5))/(2)`

B

`(3+sqrt(5))/(2)`

C

`(5-sqrt(3))/(2)`

D

`(5+sqrt(3))/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `cos^(-1)sqrt(5)/3=theta`. Then, `costheta =sqrt(5)/3`.
`tan1/2(cos^(-1)sqrt(5)/3)=tan1/2theta=(sin(theta/2))/(cos(theta/2))`.
`=sqrt((1-costheta)/(1+costheta))={(1-sqrt(5)/3)/(1+sqrt(5)/3)}^(1//2)`
`((3-sqrt(5))/(3+sqrt(5)))^(1//2)={(3-sqrt(5))/(3+sqrt(5)) xx (3-sqrt(5))/(3-sqrt(5))}^(1//2)=(3-sqrt(5))/(2)`.
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