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Q asked in Science & MathematicsMathematics · 8 years ago

Establish the identity?

[(sin^3)x + (cos^3)x] / sinx + cosx = 1 - sinxcosx

How do you prove that one equals the other?

1 Answer

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  • J
    Lv 5
    8 years ago
    Favorite Answer

    sin ^3 x + cos^ 3 x

    = (sin x + cos x)(sin ^2 x - sin x cos x + cos^2 x) ( a^3 - b^3 formula

    = ( sin x + cos x)(1- sin x cos x)

    hence

    ( sin ^3 x + cos ^3 x)/( sin x + cos x) = 1- sin x cos x

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