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Verified Answer :

MissPhiladelphia

From the given identity sin(x)+sin^2(x)=1

so
sin(x)=cos^2(x) (by cos^2(x)+sin^2(x)=1)

then
cos^12(x)+3cos^10(x)+3cos^8(x)+cos^6(x)

can be written as

sin^6(x)+3sin^5(x)+3sin^4(x)+sin^3(x)
=(sin^2(x)+sin(x))^3
=1^3
=1

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