Question

What is the equation of the tangent line of `f(x)=cosx-e^x/sinx` at `x=pi/3`?

Answer 1

`y=(-sqrt(3)/2+2/3*e^(pi/3)-2e^(pi/3))/sqrt(3)x+1/2-2e^(pi/3)/sqrt(3)-1/3*(-sqrt(3)/2+2/3*e^(pi/3)-2e^(pi/3)/sqrt(3))*pi`

Explanation:

We get
`f(pi/3)=1/2-2e^(pi/3)/sqrt(3)`

`f'(pi/3)=-sqrt(3)/2+2e^(pi/3)/3-2e^(pi/3)/sqrt(3)`