Помогите, прошуу 1)tg20° + tg40° 2)tg п/3 - tg п/4 3)1 + 2cos t 4)cos t + sin t

Question

Помогите, прошуу
1)tg20° + tg40°
2)tg п/3 - tg п/4
3)1 + 2cos t
4)cos t + sin t

Answer 1

Решение
)tg20° + tg40° = sin(20° - 40°) / [cos20°sin40°] =
= - 2sin20° / [cos20° * 2sin20°cos20°] = - 1/cos²20°
2) tg п/3 - tg п/4 = 1/√3 - 1 = (1-√3)/√3 = [(1-√3)*√3] / 3
3)1 + 2cos t = (1 + cost) + cost = 2cos²(t/2) + 2cos²(t/2) - 1=
= 4cos²(t/2) - 1
4)cos t + sin t = √2(cos45° - t)