Question

Помогите с тригонометрией,нужно найти значение выражения: sin57cos27+cos57sin27= 2sin 75-cos75=

Answer 1

Sin57cos27+cos57sin27= sin(57 + 27) = sin(84) ≈ 0.99 
sin57cos27-cos57sin27= sin(57 - 27) = sin(30) = 1/2
2sin 75*cos75=  sin2*75 = sin150 = sin(180 - 30) = sin30 = 1/2

2sin 75 - cos75 = 2si + 45) – cos(30 + 45) = 2sin30cos45 + 2cos30sin45 – cos30cos45 + sin30sin45 = 2*(1/2)*(√2/2)  + 2*(√3/2)*(√2/2)  - (√3/2)*(√2/2) + (1/2)* (√2/2) = 3√2/4 - √6/4