Question

prove that sin^2 42° - sin^2 12° = √5+1/8

​

Answer 1

sin2 42° – cos2 78° = sin2 (90° – 48°) – cos2 (90° – 12°) = cos2 48° – sin2 12° [since, sin (90 – A) = cos A and cos (90 – A) = sin A] As we know, cos (A + B) cos (A – B) = cos2A – sin2B Now the above equation becomes, = cos2 (48° + 12°) cos (48° – 12°) = cos 60° cos 36° [since, cos 36° = (√5 + 1)/4] = 1/2 × (√5 + 1)/4 = (√5 + 1)/8 = RHS Thus proved.Read more on Sarthaks.com - https://www.sarthaks.com/659011/prove-that-sin-2-42-cos-2-78-5-1-8