Calculus of a Single Variable, Chapter 2, 2.3, Section 2.3, Problem 67

You need to evaluate the equation of the tangent line to the curve f(x) = tan x , t the point ((pi)/4, 1), using the following formula, such that:
f(x) - f((pi)/4) = f'((pi)/4)(x - (pi)/4)
Notice that f((pi)/4) = 1.
You need to evaluate f'(x) and then f'((pi)/4):
f'(x) = (tan x)'
f'(x) = 1/(cos^2 x) => f'((pi)/4) = 1/(cos^2((pi)/4))
Since cos ((pi)/4) = sqrt2/2 => (cos^2((pi)/4)) = 2/4 = 1/2
f'((pi)/4) = 1/(1/2) => f'((pi)/4) = 2
You need to replace the values into the equation of tangent line:
f(x) - 1 = 2(x - (pi)/4)
Hence, evaluating the equation of the tangent line to te given curve , at the given point, yields f(x) = 2x - (pi)/2 + 1.