BuyFind

Single Variable Calculus: Concepts...

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

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)=cosxcosysinxsiny 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.

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