(3sinα+2cosα)²+(2sinα-3cosα)²=9sin²α+12sinαcosα+4cos²α+4sin²α-12
sinαcosα-9cos²α=13sin²α-5cos²α
cosβ*tgβ/sin²β-ctgβ*cosβ=(cosβ*sinβ)/(sin²β*cosβ)-cosβ*cosβ/sinβ=1/sinβ-cos²β/sinβ=(1-cos²β)/sinβ=sin²β/sinβ=sinβ
2tgα-tg(α-π)+ctg(3π/2-α)=2tgα-(tgα-tgπ)/(1+tgα*tgπ)+(ctg3π/2*ctgα+1)/(ctgα-ctg3π/2)=2tgα-tgα+1/ctgα=tgα+tgα=2*tgα