Question

(sin A+ cos A)(1-sin A cos A) = sin^3+cos^3 A
Prove that LHS is equals to RHS

Answer 1

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Answer 2

Hey dear friend

Taking R.H.S.

Sin³A+Cos³A
[By Id. (a³+b³)=(a+b)(a²+b²-ab)]

=>(SinA+CosA)(Sin²A+Cos²A-SinA CosA)

[By Id. (Sin²A+Cos²A=1)]

=>(SinA+CosA)(1-SinA CosA)

(SinA+CosA)(1-SinA CosA)=(SinA+CosA)
(1-SinA CosA)

As L.H.S.= R.H.S.

Hence Proved

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