sin2xcosx+cos2xsinx=1
Use the double angle identities, I have used the sin form of cos(2x) because I want to eliminate cos
$\displaystyle 2\sin(x)\cos(x)\cos(x) + (1- 2\sin^2(x))\sin(x) = 1 \implies 2\sin(x) \cos^2(x) + \sin(x) - 2\sin^3(x) = 1$
Of course $\displaystyle \cos^2(x) = 1-\sin^2(x)$ and hence we have
$\displaystyle 2\sin(x) (1-\sin^2(x)) + \sin(x) - 2\sin^3(x) = 1 \implies 2\sin(x) - 2\sin^3(x) + \sin(x) - 2\sin^3(x) = 1$