Answer
The tangent line formula is:
$y=x+1$
Work Step by Step
First derivate the function
$y'=\cos(x)-\sin(x)$
Then substitute the given point in the derivate. The derivate represents the slope of the curve in any point
$y'(0,1)=\cos(0)-\sin(0)=1$
So we have that $m=y'=1$
Remember the rect line formula $y=mx+b$
Let's find b (the displacement)
$b=y-mx=(1)-(1)(0)=1$
So the tangent line formula is:
$y=x+1$
