# To prove: The addition formula cos ( x + y ) = cos x cos y − sin x sin y by using the subtraction formula.

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter C, Problem 44E
To determine

## To prove: The addition formula cos(x+y)=cosxcosy−sinxsiny by using the subtraction formula.

Expert Solution

### Explanation of Solution

The subtraction formula is given as cos(αβ)=cosαcosβ+sinαsinβ.

Simplify the expression cos(x+y) as follows.

cos(x+y)=cos(x(y))=cosxcos(y)+sin(x)sin(y)=cosxcosy+sinx(siny)[cos(θ)=cosθ,sin(θ)=sinθ]=cosxcosysinxsiny

That is, cos(x+y)=cosxcosysinxsiny.

Hence the proof.

### Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!