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=tgα*ctgα+tgα-ctgα-1=tgα-ctgα
sinα = a/c
cosα = b/c
tgα = a/c
ctgα = b/a tgα możemy zapisać także w postaci sinα / cosα
tgα = sinα/cosα
ctgα = cosα/sinα
ctgα = 1/tgα
tgα = 1/ctgα
sin²α+cos²α= 1
(tgα-1)(ctgα+1) = (sinα/cosα-1)(cosα/sinα+1) = 1-cosα/sinα+sinα/cosα-1=
-cosα/sinα+sinα/cosα=-ctgα+tgα=tgα-ctgα
równość prawdziwa
tgα+ctgα=sinα/cosα+cosα/sinα=(sin²α+cos²α)/sinαcosα=1/sinαcosα
równość prawdziwa