1) (cos75'-sin75') ^2

2) вычислите sin2 альфа если sinальфа=4/5

(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