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

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Answer 1 · 2016-10-09T13:43:48

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

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

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

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

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

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

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

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