Odpowiedź:
sinα = √2/3
sin²α = (√2/3)² = 2/9
1 - cos²α = 2/9
cos²α = 1 - 2/9 = 7/9
cosα = √(7/9) = √7/3
sinα/(1 + cosα) + cosα/sinα = √2/3 : (1 + √7/3) + √7/3 : √2/3 =
= √2/3(1 + √7/3) + √7/3 * 3/√2 = √2/(3 + √7) + √7/√2 =
= √2(3 - √7)/[(3 + √7)(3 - √7)] + √7/√2 =
= √2(3 - √7)/(9 - 7) + √7/√2 = √2(3 - √7)/2 + √7 * √2/2 =
= √2(3 - √7)/2 + √14/2 = [3√2 - √(2 * 7) + √14]/2 =
= (3√2 - √14 + √14)/2 = 3√2/2
