prove that 

cos(x+y)cos(x-y)=cos^2x-sin^2y  (right hand side reads cos squared x -
sin squared y)

using sum and difference formulas and showing all work.

Hi,

Thank you for your question.

The following are well known formulas:
1) cos(A+B) = cos A cos B - sin A sin B
2) cos(A-B) = cos A cos B + sin A sin B
3) cos^2(x) + sin^2(x) = 1
4) (a+b)(a-b) = a^2 - b^2

If your question is related to schoolwork, I urge you at this point to
attempt the question. The previous 4 formulas are all you need to
solve your problem.

If you're still stuck, try going through the following solution 1 step
at a time and try and find the following line on your own. I've
deliberately left a lot of spaces between each line to facilitate
that.





So starting off with the left hand side of your equation:

cos(x+y)cos(x-y) = (cos(x)cos(y) - sin(x)sin(y))(cos(x)cos(y) + sin(x)sin(y)) 
using 1)








                 = cos^2(x)cos^2(y) - sin^2(x)sin^2(y)
using 4)








                 = cos^2(x)(1 - sin^2(y)) - (1 - cos^2(x))sin^2(y)
using 3)








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








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


I hope this helps, if you need any more help or explanations please do
not hesitate to ask.

Thanks.
endo


Search strategy:

cos(a+b)
://www.google.com/search?hl=en&lr=&ie=ISO-8859-1&safe=off&q=cos%28a%2Bb%29

Formula for sin(A+B)
http://www.ies.co.jp/math/java/trig/kahote/kahote.html