Question

Помогите пожалуйста 2
30 баллов!!! ​

Answer 1

Ответ:

Пошаговое объяснение:

1.

1) sin150°=sin(90°+60°)=cos60°=0,5.

2) cos(5π/3)=cos((6π/3)-(π/3))=cos(2π-(π/3))=cos(π/3)=0,5.

2. cosα=5/13     0<α<π/2   sinα=?   cos(2α)=?

sin²α+cos²α=1

sin²α=1-cos²α

sinα=√(1-cos²α)=√(1-(5/13)²)=√(1-(25/169))=√((169-25)/169)=

=√(144/169)=12/13.

cos(2α)=cos²α-sin²α=(5/13)²-(12/13)²=(25/(169)-(144/169)=-119/169.

3.

(sin(α-β)+sinβ*cosα)/tgα=(sinα*cosβ-sinβ*cosα+sinβ*cosα)/tgα=

=(sinα*cosβ)/(sinα/cosα)=cosα*cosβ.