1) числитель = Sinα -1
знаменатель = Cos²α = 1 - Sin²α = (1-Sinα)(1+Sinα)=-(Sinα-1)(1+Sinα)
после сокращения ответ:-1/(1 + Sinα)
2)Sin(π/4 +β) = Sinπ/4Cosβ + Cosπ/4Sinβ = √2/2 Cosβ + √2/2 Sinβ=
=√2/2(Cosβ + Sinβ)
3)Sinα - ?
4)Cos11π/12 -Cos5π/12 = -2Sin4π/3*Sinπ/4 = -2*(√3/2)*√2/2 = √6/2
5)Sin7π/12 - Sinπ/12 = 2Sinπ/4*Cosπ/3 = 2*√2/2*1/2= √2/2
6) Sin105° + Sin165° = 2Sin135°*Cos30°=2*√3/2*√3/2 = √6/2
7)Cos²15 °- Sin²15° = Cos30° = √3/2
8) (Cos75° - Sin75°)² = Cos²75°-2Sin75°Cos75° + Sin²75°=1 - Sin150° =
=1- Sin30°= 1 - 1/2 = 1/2
9)Cos(3π/2 + α) = Sinα