If sinx+sin^2x=1 then what is the value of

cos^12x+3cos^10x+3cos^8x+cos^6x

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