Answer 1

1
We have: 
\[ \sin^6 A + \cos^6 A + 3\left( \sin^2 A \right) \left( \cos^2 A \right)\]
\[ = \left( \sin^2 A \right)^3 + \left( \cos^2 A \right)^3 + 3\left( \sin^2 A \right) \left( \cos^2 A \right) \times 1\]
\[ = \left( \sin^2 A \right)^3 + \left( \cos^2 A \right)^3 + 3\left( \sin^2 A \right) \left( \cos^2 A \right)\left( \sin^2 A + \cos^2 A \right)\]
\[ = \left( \sin^2 A + \cos^2 A \right)^3 \]
\[ = 1^3 = 1\]