SOLUTION: prove (cosx^3-sinx^3)/(cosx-sinx)=(cosx^2)/(sinx+cosx)

Question 1045197: prove (cosx^3-sinx^3)/(cosx-sinx)=(cosx^2)/(sinx+cosx)
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
prove (cosx^3-sinx^3)/(cosx-sinx)=(cosx^2)/(sinx+cosx)
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I'll assume you mean cos^3(x), etc, not cos(x^3)
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(cosx^3-sinx^3)/(cosx-sinx)=(cosx^2)/(sinx+cosx)
cos^2 + sin*cos + sin^2 = cos^2/(sin+cos)
1 + sin*cos = cos^2/(sin+cos)
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At x = 45 degs:
1 + 1/2 =? (1/2)/sqrt(2)
Not an identity.

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