Question

Fie x apartine (0,π/2) y apartine (π/2,π),cos x=1/5 siny=2/3 .Sa se calculeze sin 2x cos (x-y) cos (π-y)

Answer 1

Salut!

Folosesti formula fundamentala a trigonometriei: (sin t)^2 + (cos t)^2 = 1;

Mai tii cont de faptul ca: sin x > 0; cos y < 0;

Obtii asa: sin x = $\frac{2\sqrt{6}}{5} ;$ si cos y = - $\frac{\sqrt{5}}{3} ;$

Mai departe, sin 2x = 2sinxcosx;

cos (x - y) = cos x· cos y + sin x· sin y;

cos (π - y) = - cos y;

La final, obtii asa: sin 2x = $\frac{2\sqrt{6}}{25} ;$

cos (π - y) = $\frac{\sqrt{5}}{3} ;$

cos (x - y) = $\frac{(-\sqrt{5}+4\sqrt{6})}{15} .$