Question

Sin^6A + cos^6A + 3sin^2Acos^2A = 1

Answer 1

(sin^2A)^3 + (cos^2A)^3 + 3(sin^2A)(cos^2A)(sin^2A + cos^2A)=1  

=(sin^2A+cos^2A)^3=1  

=1^3=1  

=1=1  

LHS=RHS  

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Answer 2

sin^2A + cos^2A =1

Cubing on both sides

(sin^2A+cos^2A)^3=1^3

(sin^2A)^³+(cos^2A)^3 + 3sin^2Acos^2A(sin^2A+cos^2A)=1

sin^6A+cos^6A+3sin^2Acos^2A(1)=1