Question

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

Answer 1

\[(a+b)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3}\]
and
\[\cos^{2}(x)+\sin^{2}(x)=1\]
May be useful

Answer 2

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