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Question
sin6 A + cos6 A + 3 sin2 A cos2 A =
Options
0
1
2
3
Solution
1
We have:
\[ \sin^6 A + \cos^6 A + 3\left( \sin^2 A \right) \left( \cos^2 A \right)\]
\[ = \left( \sin^2 A \right)^3 + \left( \cos^2 A \right)^3 + 3\left( \sin^2 A \right) \left( \cos^2 A \right) \times 1\]
\[ = \left( \sin^2 A \right)^3 + \left( \cos^2 A \right)^3 + 3\left( \sin^2 A \right) \left( \cos^2 A \right)\left( \sin^2 A + \cos^2 A \right)\]
\[ = \left( \sin^2 A + \cos^2 A \right)^3 \]
\[ = 1^3 = 1\]
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