вычислить tg9° - tg 27° - tg63° + tg81°

   1. Воспользуемся формулами:

• tg(π/2 - a) = ctga;
• sin(π/2 - a) = cosa;

• sin(2a) = 2sina * cosa;
• sina - sinb = 2sin((a - b)/2) * cos((a + b)/2);

• x = tg9° - tg27° - tg63° + tg81°;
• x = tg9° - tg27° - ctg27° + ctg9°;
• x = sin9°/cos9° - sin27°/cos27° - cos27°/sin27° + cos9°/sin°9.

   2. Приведем дроби к общему знаменателю:

• x = (sin^2(9°) + cos^2(9°))/(sin9°cos9°) - (sin^2(27°) + cos^2(27°))/(sin27°cos27°);
• x = 1/(sin9°cos9°) - 1/(sin27°cos27°);
• x = 2/sin18° - 2/sin54°;
• x = 2(sin54° - sin18°)/(sin18°sin54°);
• x = 4sin18°cos36°/(sin18°cos36°);
• x = 4.

   Ответ: 4.