Question

Sin(a+60)sin(a-60)-sin^2a помогите решить

Answer 1

Вспоминаем формулу sin(a + b) = sin(a)cos(b) - sin(b)cos(a)

sin(a + 60°)sin(a - 60°) = (sin a cos 60° + cos a sin 60°)(sin a cos 60° - cos a sin 60°) = sin^2 a cos^2 60° - cos^2 a sin^2 60° = sin^2 a * 1/4 - cos^2 a * 3/4 = sin^2 a * 1/4 - (1 - sin^2 a) * 3/4 = sin^2 a - 3/4

sin^2 a - 3/4 - sin^2 a = -3/4