Question

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Answer 1

Решение
№ 104.
  (tg³x - tg³y) / [(1 + tgxtgy)(tg²x + tgxtgy + tg²y)] = 
= [(tgx - tgy)*(tg²x + tgxtgy + tg²y)] /  [(1 + tgxtgy)(tg²x + tgxtgy + tg²y)] = 
= (tgx - tgy) / (1 + tgxtgy) = tg(x - y)
№105.
(cos⁴2a - sin⁴2a) / (cos4a) - (cos2a - sin2a)² =
=  [(cos²2a - sin²2a) * (cos²2a + sin²2a)] / (cos4a) - (cos²2a - 2sin2acos2a + sin²2a) = (cos²2a - sin²2a) / cos4a - 1 +  2sin2acos2a =
=  cos4a / cos4a -1 + sin4a = 1 - 1 +  sin4a = sin4a
№ 106.
[ 1/(1 - tgx) - 1/(1 + tgx)] * (cos²x - sin²x) =
 = (1 + tgx - 1 + tgx)*cos2x / (1 - tg²x) =
 = [2tgx*(1 - tg²x)] (1 - tg²x)(1 + tg²x)] = 2tgx / (1 + tg²x) = sin2x