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