How do you prove? #Sin^3A+cos^3# = #(sinA+cosA) (1-SinA*cosA)#

1 Answer
Jim G.
Mar 27, 2018

#"see explanation"#

Explanation:

#"note that"#

#a^3+b^3=(a+b)(a^2-ab+b^2)#

#"here "a=sinA" and "b=cosA#

#rArrsin^3A+cos^3A#

#=(sinA+cosA)(sin^2 A-sinAcosA+cos^2A)#

#[sin^2A+cos^2A=1]#

#=(sinA+cosA)(1-sinAcosA)="right side"#

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