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sin6 A + cos6 A + 3sin2A cos2A =A) 1 B) -1 C) 0 D) None |
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Answer» Correct option is: A) 1 \(Sin^6 A + cos^6 A + 3\, sin^2 A \, cos^2 A\) = \((Sin^2A + cos^2A)^3 - 3\, sin^2 A \, cos^2 A (Sin^2 A + cos^2 A) + 3\, sin^2A \, cos^2A\) (\(\because\) \(a^6 + b^6 = (a^2 + b^2 )^3 - 3 \, a^2 b^2 (a^2+b^2)\)) = \(1^3 - 3\, sin^2A \, cos^2A + 3\, sin^2A\, cos^2A\) (\(\because\) \(sin^2A + cos^2A = 1\)) = 1 Correct option is: A) 1 |
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