Given that θ \theta\,θ is small, use the small angle approximation of cosθ \cos \theta\,cosθ to show that
4cos(θ)+cos2(2θ)≈5−6θ2+4θ4 4 \cos(\theta) + \cos^2(2\theta) \approx 5 - 6\theta^2 + 4\theta^4 4cos(θ)+cos2(2θ)≈5−6θ2+4θ4Hence find an approximation of 4cos(θ)+cos2(2θ)4 \cos(\theta) + \cos^2(2\theta)4cos(θ)+cos2(2θ) when θ=3∘\theta = 3^\circθ=3∘
Calculate the percentage error in your approximation