#### To determine

**To find:** An equation of the tangent line to the curve y at the point.

#### Answer

The equation of the tangent line is, y=x−π−1_ at (π,−1).

#### Explanation

**Given:**

The function is, y=cosx−sinx at the point (π,−1).

**Formula used:**

**Difference Rule:**

If f(x) and g(x) are both differentiable function, then difference rule is,

ddx[f(x)−g(x)]=ddx[f(x)]−ddx[g(x)] (1)

The slope of the tangent line *y* is dydx=m at x1 (2)

The equation of tangent line is, (y−y1)=m(x−x1) at the point (x1,y1) (3)

**Calculation:**

Find derivative of the function y=cosx−sinx using Difference Rule as shown in equation (1).

ddx[cosx−sinx]=ddx[cosx]−ddx[sinx]=(−sinx)−(cosx)=−(sinx+cosx)

In equation (2), substitute the value −(sinx+cosx) for dydx.

m=−(sinx+cosx)

Substitute π for *x*.

m=−(sinπ+cosπ)=−(0−1)=1

Then the slope of the tangent line is 1.

The equation of tangent line is *y* at the point (π,−1) is calculated using equation (3).

In equation (3), substitute –1 for y1, π for x1, and 1 for *m*.

(y+1)=1(x−π)y+1=x−πy=x−π−1

Thus, the equation of the tangent line is y=x−π−1_ at (π,−1).