Reve that \( \sin ^{6} \theta+\cos ^{6} \theta+3 \sin ^{2} \theta \cos

1.	Reve that \( \sin ^{6} \theta+\cos ^{6} \theta+3 \sin ^{2} \theta \cos ^{2} \theta=1 \)
Answer» \(sin^6\theta + cos^6\theta + 3sin^2\theta cos^2\theta \) \(= sin^6\theta + cos^6\theta + 3sin^2\theta cos^2\theta(sin^2\theta + cos^2\theta)\) \(= (sin^2\theta + cos^2 \theta )^3\) \((\because (a + b)^3 = a^3 + b^3 + 3ab (a + b))\) \(= 1^3\) \(= 1\) Hence proved.

Reve that \( \sin ^{6} \theta+\cos ^{6} \theta+3 \sin ^{2} \theta \cos ^{2} \theta=1 \)

Answer»

\(sin^6\theta + cos^6\theta + 3sin^2\theta cos^2\theta \)

\(= sin^6\theta + cos^6\theta + 3sin^2\theta cos^2\theta(sin^2\theta + cos^2\theta)\)

\(= (sin^2\theta + cos^2 \theta )^3\) \((\because (a + b)^3 = a^3 + b^3 + 3ab (a + b))\)

\(= 1^3\)

\(= 1\)

Hence proved.

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Reve that \( \sin ^{6} \theta+\cos ^{6} \theta+3 \sin ^{2} \theta \cos ^{2} \theta=1 \)

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