Question

cos8θ cos2θ = cos^2 5θ - sin^2 3θ​
prove that​​

Answer 1

Answer:

Taking LHS = sin8 θ – cos8 θ = (sin4 θ)2 – (cos4 θ)2 = (sin4 θ – cos4 θ)(sin4 θ+ cos4 θ ) [∵ (a2 – b2) = (a + b) (a – b)] = {(sin2 θ)2 – (cos2 θ)2}{(sin2 θ)2 + (cos2 θ)2} = (sin2 θ + cos2 θ) (sin2 θ – cos2 θ) [(sin2 θ + cos2 θ) – 2 sin2 θ cos2 θ] [ ∵ (a2 + b2) = (a +b)2 – 2ab] = (1)[ sin2 θ –cos2 θ][(1) – 2 sin2 θ cos2 θ] = (sin2 θ – cos2 θ)(1 – 2 sin2 θ cos2 θ) = RHSRead more on Sarthaks.com - https://www.sarthaks.com/930318/prove-that-the-following-identities-sin-8-cos-8-sin-2-cos-2-1-2sin-2-cos-2