##### cos(x+y)-sin(x-y)=2cosxsiny

 Calculus Tutor: None Selected Time limit: 1 Day

Simplify the expression by using the Double-Angle Formula

May 15th, 2015
Please check if the question is

Sin (x+y) + Sin (x-y)

May 15th, 2015

I mean Sin (x+y) - Sin (x-y)

May 15th, 2015

## sin(x + y) - sin(x - y) = 2cos(x)sin(y)  sin(x)cos(y) + cos(x)sin(y) - (sin(x)cos(y) - cos(x)sin(y)) = 2cos(x)sin(y)  sin(x)cos(y) + cos(x)sin(y) - sin(x)cos(y) + cos(x)sin(y) = 2cos(x)sin(y)  2cos(x)sin(y) = 2cos(x)sin(y)  So that verifies the identity

May 15th, 2015

What is:
cos(x+y)cos(x-y)=cos(^2)x-sin(^2)y

May 15th, 2015

so u have posted

## cos(x+y)-sin(x-y) instead of sin(x + y) - sin(x - y)

May 15th, 2015

Yes, the first question is solved and I have moved onto another question.

It asks: Prove the cofuntion identity using the Addition and Subtraction Formulas.
cos(x+y)cos(x-y)=cos(^2)x-sin(^2)y

May 15th, 2015

cos(x+y)cos(x-y) = (cosxcosy-sinxsiny) (cosxcosy+sinxsiny)

= cos(^2)xcos(^2)y- sin(^2)xsin(^2)y

=  (1-sin(^2)x) cos(^2)y- sin(^2)xsin(^2)y

= cos(^2)y-sin(^2)x cos(^2)y- sin(^2)xsin(^2)y

= cos(^2)y-sin(^2)x (cos(^2)y + sin(^2)y)

= cos(^2)y-sin(^2)x(1)

= cos(^2)y-sin(^2)x

= 1- sin(^2)y-1+cos(^2)x

= cos(^2)x-sin(^2)y

= RHS

Please let me know if you have any questions and best me if you are satisfactory.

May 15th, 2015

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May 15th, 2015
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May 15th, 2015
May 28th, 2017
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