Tga+ctgb/tgb+ctga=tga*ctgb

Question

Tga+ctgb/tgb+ctga=tga*ctgb

Answer 1

1. tgα+ctgβ=sinα/cosα+cosβ/sinβ=(sinαsinβ+cosβcosα)/(cosαsinβ)

2. tgβ+ctgα=sinβ/cosβ+cosα/sinα=(sinβsinα+cosαcosβ/(cosβsinα)

3. [(sinαsinβ+cosβcosα)/(cosαsinβ)] / [(sinβsinα+cosαcosβ)/(cosβsinα)]=(cosβsinα)/(cosαsinβ)
tgα*ctgβ
4. tgα*ctgβ=tgα*ctgβ

Answer 2

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