Question #a30c5

1 Answer
Aug 12, 2017

y=1

Explanation:

  1. Find the derivative of the function using the quotient rule:
    #dy/dx = ((1+cosx)(cosx)-(sinx)(1-sinx))/(1+cosx)^2#
  2. Find the instantaneous rate of change of the tangent line at the point #pi/2# by plugging in #x=pi/2# and solving for #dy/dx#.
    #dy/dx = m = ((1+0)(0)-(1)(1-1))/(1+0)^2 = 0#
  3. Write the general equation for a line:
    #y-y_1=m(x-x_1)#
  4. Solve for y_1 by plugging in #x=pi/2# into the original equation and solving for y
    #y_1=sinx/(1+cosx)#
    #y_1=1/(1+0)=1#
  5. Solve for the equation of the tangent line with point #(pi/2, 1)#
    #y-1=0(x-(pi/2))#
    #y=1#