Odpowiedź:
a)
sinα = 1/5
sin²α = (1/5)² = 1/25
cos²α = 1 - sin²α = 1 - 1/25 = 25/25 - 1/25 = 24/25
cosα = √(24/25) = √(4 * 6)/5 = 2√6/5
tgα = sinα/cosα = 1/5 : 2√6/5 = 1/5 * 5/2√6 = 1/2√6 = √6/(2 * 6) =
= √6/12
ctgα = 1/tgα = 12/√6 = 12√6/6 = 2√6
b)
tgα = 2 i 2/3 = 8/3
ctgα = 1/tgα = 3/8
tg²α = (8/3)² = 64/9
sin²α/cos²α = 64/9
9sin²α = 64cos²α
9sin²α = 64(1 - sin²α) = 64 - 64sin²α
9sin²α + 64sin²α = 64
73sin²α = 64
sin²α = 64/73
sinα = √(64/73) = 8/√73 = 8√73/73
9(1 - cos²α) = 64cos²α
9 - 9cos²α = 64cos²α
- 9cos²α - 64cos²α = - 9
- 73cos²α = - 9
73cos²α = 9
cos²α = 9/73
cosα = √(9/73) = 3/√73 = 3√73/73
