Question

Вычислите sin⁡2x,cos⁡2x,tg 2x,ctg 2x, если cos⁡x=5/13,xϵ [0,π/2]

Answer 1

cos⁡x=5/13,xϵ [0,π/2]
sinx=√(1-(5/13)²)=√(169-25)/169=√144/169=12/13
sin2x=2sinxcosx=2*5/13*12/13=24*5/169=120/169
cos2x=cos²x-sin²x=(5/13)²-(12/13)²=(25-144)/169=-119/169
tg2x=(120/169):(-119/169)=-120/119
ctg2x=-119/120