Question

prove that (sin A+cos A)(1-3sin^2 A.cos^2 A)=sin^3 A+cos^3 A

Answer 1

Hi ,

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We know the algebraic identity ,

a³ + b = ( a + b ) ( a² + b² - ab )

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sin³ A + cos³ A

= ( sinA + cosA ) ( Sin² A+cos² A- SinAcosA )

= ( sinA + cosA ) ( 1 - sinAcosA )

I hope this helps you.

:)