Odpowiedź:
5tgα = 1
tgα = 1/5
tg²α = (1/5)² = 1/25
sin²α/cos²α = 1/25
25sin²α = cos²α = 1 - sin²α
25sin²α + sin²α = 1
26sin²α = 1
sin²α = 1/26
sinα = √(1/26) = 1/√26 = √26/26
sinα/cosα = 1/5
cosα = 5sinα = 5√26/26
- 3sinα = - 3 * √26/26 = - 3√26/26
cosα = 5√26/26
5cosα + 4sinα = 5 * 5√26/26 + 4 * √26/26 = 25√26/26 + 4√26/26 =
= 29√26/26
(- 3sinα + cosα)/(5cosα + 4sinα) =
= ( -3√26/26 + 5√26/26) : 29√26/26 = 2√26/26 * 26/29√26 =
= 2/29
