solve cos3 theta + 8 cos ^ 3 theta =0 Share with your friends Share 1 Neha Sethi answered this Dear student We have,cos3θ+8cos3θ=0⇒cos3θ-3cosθsin2θ+8cos3θ=0⇒9cos3θ-3cosθsin2θ=0⇒3cosθ3cos2θ-sin2θ=0⇒3cosθ3cosθ-sinθ3cosθ+sinθ=0Case1: when cosθ=0⇒θ=π2+nπ,n∈ZCase2: 3 cosθ-sinθ=0⇒3-tanθ=0⇒3=tanθ⇒tanθ=tanπ3⇒θ=π3+nπ,n∈ZCase3: 3cosθ+sinθ=0⇒3+tanθ=0⇒tanθ=-3⇒tanθ=tan2π3⇒θ=2π3+nπ,n∈ZPlugging all cases, we getθ=π2+nπ,θ=π3+nπ,θ=2π3+nπ, where n∈Z Regards 1 View Full Answer
