cos2(θ+ϕ)+4cos(θ+ϕ)sinθsinϕ+2sin2ϕ=cos2(θ+ϕ)+2cos(θ+ϕ)[2sinθsinϕ]+2sin2ϕ=cos2(θ+ϕ)+2cos(θ+ϕ)[cos(θ−ϕ)−cos(θ+ϕ)]+2sin2ϕ=cos2(θ+ϕ)+2cos(θ+ϕ)cos(θ−ϕ)−cos2(θ+ϕ)+2sin2ϕ=[2cos22(θ+ϕ)−1]+cos(θ+ϕ+θ−ϕ)+cos(θ+ϕ−θ+ϕ)−2cos2(θ+ϕ)+2sin2ϕ=−1+cos2θ+cos2ϕ+(1−cos2θ)=cos2ϕ