Calculus of a Single Variable, Chapter 2, 2.3, Section 2.3, Problem 61

You need to evaluate the equation of the tangent line to the curve f(t) =(sec t)/t , at the point (pi, -1/(pi)), using the following formula, such that:
f(t) - f(pi) = f'(pi)(t - pi)
Notice that f(pi)=1/(pi).
You need to evaluate f'(t), using the quotient rule, and then f'(pi):
f'(t) = ((sec t)'*t- (sec t)*(t)')/(t^2)
f'(t) = (t*sec t*tan t - sec t)/(t^2)
f'(pi)= (pi*1/(cos pi)* tan pi - 1/(cos pi))/(pi^2)
cos pi = -1 and tan pi = 0
f'(pi)= (1)/(pi^2)
You need to replace the values into the equation of tangent line:
f(t) - 1/(pi) = (1)/(pi^2)*(t - pi)
f(t) = 1/(pi) + t/(pi^2) - 1/(pi)
reducing like terms yields:
f(t) = t/(pi^2)
Hence, evaluating the equation of the tangent line to te given curve , at the given point, yields f(t) = t/(pi^2) .