can you simplify cos𝜃 − 2 sin^2 𝜃 cos 𝜃 + cos 𝜃 sin^4 𝜃

Answer 1

cosA(1-2sin^2A + sin^4A) = cosA(sin^2A-1)^2= cosA(sinA-1)^2(sinA+1)^2=

cosA(sinA-1)(sinA-1)(sinA+1)(sinA+1)

think of it as similar to x-2xy^2+xy^4 where x=cosA, and y=sinA

x(1-2y^2 + y^4) let z =y^2

1-2z+z^2 = (z-1)^2 = (y^2-1)^2=(y-1)^2(y+1)^2