Вычислите cos150 + cos75 + 2

Question

Вычислите cos150 + cos75 + 2

Answer 1

Cos150+cos75+2=cos(180-30)+cos(90-15)+2=-cos30+sin15+2=-√2/3+2+sin15=
sin15=√(1/2(1-cos30)=(√3-1)/2√2
=2-2√3+(√3-1)/2√2