SOLUTION: Prove the identity: [Sin^3(x)-cos^3(x)] / [sin(x)-cos(x)] = 1+sinx.cosx

Question 889760: Prove the identity:
[Sin^3(x)-cos^3(x)] / [sin(x)-cos(x)] = 1+sinx.cosx
Answer by dkppathak(439) (Show Source): You can put this solution on YOUR website!
[Sin^3(x)-cos^3(x)] / [sin(x)-cos(x)] = 1+sinx.cosx
we know that a^3-b^3=(a-b)(a^2+b^2+ab) using same identity
sin^3 x- cos^3 x=(sin x-cos x)(sin^2 x+ cos^2 x+cos x sin x)
we know sin^2 x+cos^2=1 by substitution
sin^3 x- cos^3 x=(sin x-cos x)(1+cos x sin x)
[Sin^3(x)-cos^3(x)] / [sin(x)-cos(x)] = (sin x-cos x)(1+cos x sin x)/(sin x- cos x) by cancelling (sin x- cos x) from numerator and denominator
[Sin^3(x)-cos^3(x)] / [sin(x)-cos(x)] = 1+sinx.cosx
proved

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