(sin^2(П/2+альфа)-cos^2(альфа-(3П/2)))/(tg^2(альфа+(3П/2))-ctg^2(альфа-П/2)) упростить...

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

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 .

Answer 2

I hope this helps you

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Comments

(sin²2α) / 4 . → описка

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

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thank you ❤️