The value of 6({sin ^6}theta + {cos ^6}theta | vedclass

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Question

(c) $6({\sin ^6}	heta + {\cos ^6}	heta ) - 9({\sin ^4}	heta + {\cos ^4}	heta ) + 4$

$ = 6[{({\sin ^2}	heta + {\cos ^2}	heta )^3} - 3{\sin ^2}

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(c) $6({\sin ^6}	heta + {\cos ^6}	heta ) - 9({\sin ^4}	heta + {\cos ^4}	heta ) + 4$

$ = 6[{({\sin ^2}	heta + {\cos ^2}	heta )^3} - 3{\sin ^2}	heta {\cos ^2}	heta ({\sin ^2}	heta + {\cos ^2}	heta )]$

$ - 9[{({\sin ^2}	heta + {\cos ^2}	heta )^2} - 2{\sin ^2}	heta {\cos ^2}] + 4$

$ = 6[1 - 3{\sin ^2}	heta {\cos ^2}	heta ] - 9\,[1 - 2{\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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