Question

1)(cos75'-sin75')^2
2)вычислите sin2альфа если sinальфа=45

Answer 1

(cos75°-sin75°)²=cos²75°-2*sin75°cos75°+sin²75°=(sin²75°+cos²75°)-sin(2*75°)=1-sin(90°+60°)=1-cos60°=1-1/2=1/2=0,5

2. sinα=4/5. sun2α=?
sin2α=2*sinα*cosα, cosα=?
sin²α+cos²α=1
(4/5)²+cos²α=1. cos²α=1-16/25. cos²α=9/25

1. α∈(0;π/2) ⇒cosα>0. cosα=3/5
sin2α=2*(4/5)*(3/5)=24/25

2. α∈(π/2;π) ⇒cosα<0. cosα=-3/5
sin2α=2*(4/5)*(-3/5)=-24/25