Question

Prove that
Cos^6 + Sin^6 = 1- 3Sin²A X Cos²A

Answer 1

Heya

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( a^6 + b^6 ) = ( a² + b² )³ - 3a²b² {a² + b²}

And

Sin² x + Cos² x = 1

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=>

{ Sin²A + Cos²A }³ - 3 { Sin² × Cos² A }

× { Sin² A + Cos² A }

=>

{ 1 }³ - 3 Sin² A × Cos² A } { 1 }

=>

1 - 3 { Sin² A × Cos² A }