SOLUTION: I have to verify the identity of (1+sin(alpha))(1-sin(alpha))=cos^2(alpha)

Question 659671: I have to verify the identity of
(1+sin(alpha))(1-sin(alpha))=cos^2(alpha)
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Start with the well known identity (you can easily prove it)
(1) sin^2(x) + cos^2(x) = 1
Now subtract sin^2(x) from each side and get
(2) cos^2(x) = 1 - sin^2(x)
Now factor the right side using the property
(3) (a^2-b^2) = (a+b)*(a-b), called the difference of two perfect squares in algebra (remember?), and get
(4) cos^2(x) = (1+sin(x))*(1-sin(x)) QED

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