Question

Упростить(тригонометрия) фото внутри

Answer 1

Получится вот так :)

Answer 2

1)   (cos²t + 1 + 2sint + sin²t) /[ (1 + sint)*cost] = (2 + 2sint) / [(1 + sint)*cost] =
 = 2 / cost
 2)  (1 + tg⁴t) / (tg²t + ctg²t) = [tg²t*(1 + tg⁴t)] / (tg⁴t + 1) = tg²t
3)  sin²t / (1 + tg²t)  + cos²t / ( 1 + ctg²t)  = sin²t / (1 + tg²t) + (tg²tcos²t) / (1 + tg²t) = (sin²t + sin²t) / ( 1 + tg²t) = 2sin²t / (1 + tg²t) = 2sin²tcos²t / (1 + sin²t) = sin²2t / [2(1 + sin²t)]