Tgα=2.4
ctgα=1/tgα=1/2.4=5/12
tgα=sinα/cosα=sinα/√(1-sin²α)
sinα/√(1-sin²α)=2.4
sinα=2.4*√(1-sin²α) возведем в квадрат
sin²α=5.76*(1-sin²α)
sin²α=5.76-5.76sin²α
6.76sin²α=5.76
sin²α=576/676
sinα=+-√(576/676)=+-(24/26)=+-12/13 поскольку 0<α<π/2<br>sinα=12/13
cosα=√(1-sin²α)=√(1-(12/13)²)=√25/169=5/13