Question

Тригонометрия. Смотрите вложение.

Answer 1

sin 3α·sin4α·cos(0.5π -7α) - cos3α·cos(0.5π+4α)·cos7α = 1/3

sin 3α·sin4α·sin7α + cos3α·sin4α·cos7α = 1/3

sin4α·(sin 3α·sin7α + cos3α·cos7α) = 1/3

sin4α·cos(7α -3α) = 1/3

sin4α·cos4α = 1/3

2sin4α·cos4α = 2/3

sin8α = 2/3

cos²8α = 1-sin²8α =1- 4/9 = 5/9

cos 16α = cos²8α - sin²8α = 5/9 - 4/9 = 1/9

ответ: cos 16α = 1/9