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

label Calculus
account_circle Unassigned
schedule 1 Day
account_balance_wallet $5

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

Did you know? You can earn $20 for every friend you invite to Studypool!
Click here to
Refer a Friend
...
May 15th, 2015
...
May 15th, 2015
Sep 23rd, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer