Prove that sin3(θ)+cos3(θ)=(sin(θ)+cos(θ))(1−sin(θ)cos(θ))\sin^3(\theta) + \cos^3(\theta) = (\sin(\theta) + \cos(\theta))(1 - \sin(\theta)\cos(\theta))sin3(θ)+cos3(θ)=(sin(θ)+cos(θ))(1−sin(θ)cos(θ)) for all θ\thetaθ.
False; the identity only holds for acute angles
True; this is a valid trigonometric identity
True; but only when sin(θ)≠0\sin(\theta) \neq 0sin(θ)=0 and cos(θ)≠0\cos(\theta) \neq 0cos(θ)=0
False; the right side should be (1+sin(θ)cos(θ))(1 + \sin(\theta)\cos(\theta))(1+sin(θ)cos(θ))