Odpowiedź:
tgα = 1,05 = 1 5/100 = 1 1/20
tg²α = (1 1/20)² = (21/20)² = 441/400
sin²α/cos²α = 441/400
sin²α = 441/400 * cos²α = 441/400(1 - sin²α) = 441/400 - 441/400 sin²α
sin²α + 441/400sin²α = 441/400 | * 400
400sin²α + 441sin²α = 441
841sin²α = 441
sin²α = 441/841
sinα = √(441/841) = 21/29
sinα/cosα = 1 1/20
21/29 : cosα = 21/20
21/29coα = 21/20
20 * 21 = 29cosα * 21
420 = 609cosα
cosα = 420/609 = 140/203
ctgα = 1/tgα = 1 : 1 1/20 = 1 : 21/20 = 1 * 20/21 = 20/21
