Need help with double angle identity questions.

[hayling123]

Hey guys,

I'm working my way through some problems and have become stuck on the following questions-

"Use the double-angle identity for tangent, and the exact value of tan(5π/6), for a different way to find an exact value of tan(5π/12)."

I have already shown the exact value of tan(5π/12) is 2+sqrt3

Any help with how i'd go about it would be great. I know I will need to solve a quadratic equation, but any help to get there would be fantastic

cheers

 

[BigBeachBanana]

[math]\tan\left(\frac{5\pi}{6}\right)=\tan\left(2\cdot\frac{5\pi}{12}\right)[/math]Can you use the double-angle identity to continue?

 

[Steven G]

I have already shown the exact value of tan(5π/12) is 2+sqrt3

Can you show how you got tan(5π/12) = 2+sqrt3?