3 $$(sin x – cos x)^4 + 6 (sin x + cos x)^2+4 (sin x)^6 + 4 (cos x)^6$$ equals to

=

$$3 (sin x – cos x)^4 + 6 (sin x + cos x)^2+4 (sin x)^6 + 4 (cos x)^6$$

=

$$3{sin^2x+cos^2x-2sinxcosx}^2+6(sin^2x+cos^2x+2sinxcosx)+4sin^6x+4cos^6x$$

=

$$3{1-2sinxcosx}^2+6(1+2sinxcosx)+ 4sin^6x+4cos^6x$$

=

$$3{1+4sin^2xcos^2x-4sinxcosx}+6(1+2sinxcosx)+4sin^6x+4cos^6x$$

=

$$3+12sin^2xcos^2x-12 sinx cosx+6+12 sinx cosx+4sin^6x+4cos^6x$$

=

$$3+12sin^2xcos^2x-12 sinx cosx+6+12 sinx cosx+4((sin^2x)^3+(cos^2x)^3)$$

=

$$3+12sin^2xcos^2x-12 sinx cosx+6+12 sinx cosx+4(sin^2x+cos^2x)^3-3sin^2xcos^2x(sin^2x+cos^2x$$

=

$$3+12sin^2xcos^2x-12 sinx cosx+6+12 sinx cosx+4(sin^2x+cos^2x)^3-12sin^2xcos^2x$$

=3+6+4 =13

Answer (C)