Question

Упростите выражение......​

Answer 1

Ответ:

Объяснение:

cos(3π/2 - 2a) / (1 + cos(2a)) · ctg(π + a) =

= cos(π + π/2 - 2a) / (1 + cos(2a)) · ctg(a) =

= - cos(π/2 - 2a) / (1 + cos(2a)) · ctg(a) =

= - sin(2a) / (1 + cos(2a)) · ctg(a) =

= - 2sin(a)cos(a) / (1 + 2cos²a - 1) · cos(a) / sin(a) =

= - 2sin(a)cos(a) / (2cos²a) · cos(a) / sin(a) =

= - sin(a) / cos(a) · cos(a) / sin(a) = - 1

Формулы:

cos(π + a) = - cos(a)

cos(π/2 - a) = sin(a)

sin(2a) = 2sin(a)cos(a)

cos(2a) = 2cos²a - 1

ctg(a) = cos(a) / sin(a)