Question

(sin^2(П/2+альфа)-cos^2(альфа-(3П/2)))/(tg^2(альфа+(3П/2))-ctg^2(альфа-П/2)) упростить выражение
П-пи
sin^2-степень
/-деление

Answer 1

I hope this helps you

Answer 2

(sin²2α) / 4 . → описка

Answer 3

ahh yes you're right :) i have to edit my answer please

Answer 4

thank you ❤️

Answer 5

task/30229370  Упростить выражение

( (sin²(π/2+α)- cos²(α -3π/2) ) / ( tg²(α+ 3π/2) - ctg²(α -π/2) )

решение  ( (sin²(π/2+α)- cos²(α -3π/2) ) / ( tg²(α+ 3π/2) - ctg²(α -π/2) ) ⇔

(sin²(π/2+α) - cos²(3π/2 -α ) ) / ( tg²(3π/2+α) - ctg²(π/2- α ) )

(cos²α - sin²α ) / ( ctg²α - tg²α) =

(cos²α - sin²α )* sin²α*cos²α / ( cos⁴α -sin⁴α) =

(cos²α - sin²α )* sin²α*cos²α / ( cos²α - sin²α)*( cos²α + sin²α) =

sin²α*cos²α = (sinα*cosα)² =( (sin2α) / 2)² = 0,25sin²2α .