10. cosπ/6*tq45° -sinπ/3*ctq45° =cos(π/2 -π/3)*tq45° -sinπ/3*tq45° =
=sinπ/3*tq45° -sinπ/3*tq45° =0 ||tq45°=ctq45° = 1||.
---иначе
cosπ/6*tq45° -sinπ/3*ctq45° =(√3)/2 * 1 - (√3)/2 * 1 =0.
-------
11. (7- sin²α -cos²α)/ (3cos²α +3sin²α) =
((7- (sin²α +cos²α)) /3(sin²α +cos²α) =(7-1)/(3*1) =6/3 =2.
-------
14. cosα =2/3 , α∈(0; π/2) .
---
sinα - ?
sin²α +cos²α =1 ⇒sinα =± √(1-cos²α) , но α∈(0; π/2) где sinα >0 , поэтому : sinα = √(1-cos²α) =√(1 -(2/3)²) = (√5)/3.