Question

Question #a30c5

Answer 1

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`