The value of 6(sin^6 theta + cos^6 theta) - 9 | vedclass

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(C) Given expression: $6(\sin^6 	heta + \cos^6 	heta) - 9(\sin^4 	heta + \cos^4 	heta) + 4$Using the identities $\sin^6 	heta + \cos^6 	heta = (

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$1$

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(C) Given expression: $6(\sin^6 	heta + \cos^6 	heta) - 9(\sin^4 	heta + \cos^4 	heta) + 4$Using the identities $\sin^6 	heta + \cos^6 	heta = (\sin^2 	heta + \cos^2 	heta)^3 - 3\sin^2 	heta \cos^2 	heta (\sin^2 	heta + \cos^2 	heta) = 1 - 3\sin^2 	heta \cos^2 	heta$ and $\sin^4 	heta + \cos^4 	heta = (\sin^2 	heta + \cos^2 	heta)^2 - 2\sin^2 	heta \cos^2 	heta = 1 - 2\sin^2 	heta \cos^2 	heta$.Substituting these into the expression:$= 6(1 - 3\sin^2 	heta \cos^2 	heta) - 9(1 - 2\sin^2 	heta \cos^2 	heta) + 4$$= 6 - 18\sin^2 	heta \cos^2 	heta - 9 + 18\sin^2 	heta \cos^2 	heta + 4$$= 6 - 9 + 4$$= 1$.

The value of $6(\sin^6 \theta + \cos^6 \theta) - 9(\sin^4 \theta + \cos^4 \theta) + 4$ is

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