Answer :

We have, 3(sin x – cos x)4 + 6 (sin x + cos x)2 + 4(sin6 x + cos6 x)


=3(sin2x+cos2x-2sin x cos x)2+6(sin2x+cos2x+2sin x cos x) +4[(sin2x)3 + (cos2x)3]


=3(1-2sin x cos x)2+6(1+2sin x cos x) +4[(sin2x+ cos2x)3 -3 sin2x cos2x(sin2x+ cos2x)]


=3(1+4 sin2x cos2x-4sin x cos x) +6+12sin x cos x+4-12sin2x cos2x


=3+12 sin2x cos2x-12 sin x cos x+6+12sin x cos x+4-12sin2x cos2x


=3+6+4


= 13


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