SOLUTION: cos^4[x]-sin^4[x]=cos^2[x]-sin^2[x] please explain stepbystep

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Question 285481: cos^4[x]-sin^4[x]=cos^2[x]-sin^2[x]
please explain stepbystep
Answer by toidayma(44) About Me  (Show Source):
You can put this solution on YOUR website!
Since a^2 - b^2 = (a-b)(a+b), apply this with a = cos^2(x) and b = sin^2(x). You have:
cos%5E4%28x%29+-+sin%5E4%28x%29 = %28cos%5E2%28x%29+-+sin%5E2%28x%29%29%28cos%5E2%28x%29+%2B+sin%5E2%28x%29%29
Since with every x, sin^2(x) + cos^2(x) = 1, therefore, you can scratch out the factor (cos^2(x) + sin^2(x)). So, cos^4(x) - sin^4(x) = cos^2(x) - sin^2(x).
Is it easy?