Explanation:
f(pi/3) = tan(pi/3) = sqrt(3)
so, one point on the tangent line is the touching point
(pi/3, sqrt(3)).
and the slope of the tangent we get from the first derivation of f(x) at x = pi/3 :
tan'(x) = sec²(x)
sec(pi/3) = 2
sec²(pi/3) = 2² = 4
so, the slope of the tangent line is 4.
the point slope form of a line is
y - y1 = a(x - x1)
with (x1, y1) being a point on the line, a being the slope.
y - sqrt(3) = 4(x - pi/3) = 4x - 4pi/3
and so the equation of the tangent line at x = pi/3 is
y = 4x - 4pi/3 + sqrt(3)