Question

If sinx+sin^2x=1 then what is the value of
cos^12x+3cos^10x+3cos^8x+cos^6x

Answer 1

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