Question

How to find an equation of the tangent line to the curve at the given point if `y=cosx-sinx` and `(pi,-1)`?

Answer 1

First evaluate the derivative of your function:
`y'(x)=-sin(x)-cos(x)`
Then evaluate the derivative at your point, i.e., at `x=pi` to find the slope `m` of the tangent line:
`m=y'(pi)=0+1=1`
Finally, use the relationship:
`y-y_0=m(x-x_0)` to find the equation of the tangent line:
`y-(-1)=1(x-pi)`
`y=x-(pi+1)`

Graphically: