Question

Show that: cos 5θ = 16 cos5θ – 20 cos3θ + 5 cosθ

Answer 1

= cos5θ

= 5C0 cos5θ – 5C2 cos3θ sin2θ + 5C4 cosθ sin4θ

= cos5θ – 10 cos3θ (1 – cos2θ) + 5 cosθ (1 – cos2θ)2

= cos5θ – 10 cos3θ + 10 cos5θ + 5 cosθ (1 – 2 cos2θ + cos4θ)

= cos5θ – 10 cos3θ + 10 cos5θ + 5 cosθ – 10 cos3θ + 5 cos5θ

= 16 cos5θ – 20 cos3θ + 5 cosθ