Question

if, tan(A-30°)=2-√3 then find A?

Answer 1

tan(a-30)=tana-(1/√3)/1+tana/√3
let tana=t
and simplify
√3t-1/√3+t=2-√3
√3t-1=(2-√3)(√3+t)
√3t-1=2√3+2t-3-√3t
-1+3=2t
t=1
tana=1
a=45 or π/4

Answer 2

tan (A-30)=tan15°
$tan15 = 2 - \sqrt{3}$

A-30=15
A=15+30
A=45°