Calculus 8th Edition

The tangent line formula is: $y=x+1$
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: $y=x+1$