Question

If `tanx=(sqrt (3)+1)/(sqrt (3)-1)`. What is x?

Answer 1

`x=npi+(5pi)/12" where "n in ZZ`

Explanation:

`tanx=(sqrt (3)+1)/(sqrt (3)-1)`.

`=>tanx=(sqrt (3)/sqrt3+1/sqrt3)/(sqrt (3)/sqrt3-1/sqrt3)`.

`=>tanx=(1+1/sqrt3)/(1-1xx1/sqrt3)`.

`=>tanx=(tan(pi/4)+tan(pi/6))/(1-tan(pi/4)xxtan(pi/6))`.

`=>tanx=tan(pi/4+pi/6)=tan((5pi)/12)`.

`=>x=npi+(5pi)/12" where "n in ZZ`