Answer to Question #16697 in Trigonometry for Mark

Question

cos(x)^(4)-sin(x)^(4)=2cos(x)^(2)-1

Answer 1

cos(x)^(4)-sin(x)^(4)=(cos(x)^(2)-sin(x)^(2)
)*(cos(x)^(2)+sin(x)^(2))= =cos(x)^(2)-sin(x)^(2)=cos(x)^(2)-(1cos(x)^(2))=2cos(x)^(2)-1
we
use here cos(x)^2+sin(x)^2=1