Question 250825: simplify the expression:
cos^4x - sin^4x /cos^2x - sin^2x
Answer by drk(1908)   (Show Source):
You can put this solution on YOUR website! the original question was:
(cos^4x - sin^4x)/(cos^2x - sin^2x)
Let's factor the numerator first. Notice it is the difference of two squares, so, we get
(cos^2(x) + sin^2(x))(cos^2(x) - sin^2(x))
Now, notice that the second parenthesis matches with the denominator. We have
(cos^2(x) + sin^2(x))(cos^2(x) - sin^2(x)) / (cos^2(x) - sin^2(x))
which cancels and gives us
(cos^2(x) + sin^2(x))
But this identity is 1.
So, our answer is simply 1.
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