Verified answer

Verified answer

Ответ:

Объяснение:

1.

a) sin150°=sin(180°-150°)=sin30°=0,5.

б) tg(3π/4)=tg135°=tg(180-45°)=-tg45°=-1.

2.

a) cos(π/2+α)+sin(π-α)=-sinα+sinα=0.

б) sin(α+β)-sinβ*cosα=sinα*cosβ+sinβ*cosα-sinβ*cosα=sinα*cosβ.

в) cos²2α+2*sin²α=cos²-sin²α+2*sin²α=sin²α+cos²α=1.

3.

2*sinα*cosα*cos(2α)=sin(2a)*cos(2α)=2*sin(2α)*cos(2α)/2=sin(4α)/2.

4.

a) (sinα-sin3α)/(cos3α+cosα)=- (sin3α-sinα)/(cos3α+cosα)=

=-2*(sin((3α-α)/2)*cos((3α+α)/2)/(2*cos((3α+α)/2)*cos((3α-α)/2))=

=-sinα*cos2α/(cos2α*cosα)=-sinα/cosα=-tgα.

б) (1-cos2α)/sin(π-α))=(sin²α+cos²α-(cos²α-sin²α))/sinα=

(sin²α+cos²α-cos²α+sin²α)/sinα=2*sin²α/sinα=2*sinα.