Question

prove that cos4 θ =4sinθ cos³θ - 4slcosθsin³θ​

Answer 1

Answer:

(cosθ + i sinθ)4 = 4C0 cos4θ + 4C1(cos3θ (i sinθ) + 4C2 cos2θ(i sinθ)2 + 4C1 cosθ (i sinθ)3 + 4C4 (i sinθ)4 = cos4θ + 4i cos3 sinθ – 6 cos2θ sin2θ – 4i cosθ sin3θ + sin4θ => cos4θ + i sin4θ = (cos4θ – 6 cos2θ sin2θ + sin4θ) + i(4 cos3θsinθ – 4 cosθ sin3θ) So, sin4θ = 4sinθcos3θ - 4cosθsin3θRead more on Sarthaks.com - https://www.sarthaks.com/489661/show-that-sin-4-4-sin-cos-3-4-cos-sin-3