Dany jest kąt α taki, że sinα=2/3. Oblicz [latex] frac{ sqrt{1 +tg ^{2} alpha } } frac{cos }{} alpha [/latex]

[latex]sin x=frac{2}{3}\\ cos^2x=1-sin^2x=1-(frac{2}{3})^2=frac{5}{9}\\ cos x = frac{sqrt{5}}{3};vee;cos x=-frac{sqrt{5}}{3}\\ tg^2x=frac{4}{5}[/latex] 1. [latex] sin x=frac{2}{3}wedge;cos x=frac{sqrt{5}}{3};wedge;tg ^2x=frac{4}{5}\\ cfrac{ sqrt{1 +tg ^{2} x}} {cos x} =cfrac{ sqrt{1 + frac{4}{5}}} {frac{sqrt{5}}{3}} =cfrac{ sqrt{frac{9}{5}}} {frac{sqrt{5}}{3}} =cfrac{3}{sqrt{5}}cdot cfrac{3}{sqrt{5}}=cfrac{9}{5} [/latex] 2. [latex] sin x=frac{2}{3}wedge;cos x=-frac{sqrt{5}}{3};wedge;tg ^2x=frac{4}{5}\\ cfrac{ sqrt{1 +tg ^{2} x}} {cos x} =cfrac{ sqrt{1 + frac{4}{5}}} {-frac{sqrt{5}}{3}} =-cfrac{ sqrt{frac{9}{5}}} {frac{sqrt{5}}{3}} =-cfrac{3}{sqrt{5}}cdot cfrac{3}{sqrt{5}}=-cfrac{9}{5} [/latex]

dany jest kąt ostry alfa taki, że [latex]sin alpha - cos alpha = frac{ sqrt{5} }{10} [/latex] Oblicz sin 2alfa

dany jest kąt ostry alfa taki, że [latex]sin alpha - cos alpha = frac{ sqrt{5} }{10} [/latex] Oblicz sin 2alfa...