• 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







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