Wartość wyrażenia

[RAFAELLO14]

Oblicz wartość wyrażenia \(\displaystyle{ \frac{x}{ \sqrt{y} }}\) jeśli \(\displaystyle{ x=sin ^{2}165°-cos ^{2}165°}\), \(\displaystyle{ y=sin195°cos195°}\)

[wb]

\(\displaystyle{ x=sin ^{2}165°-cos ^{2}165°=-cos(2 165^0)=-cos330^0=-cos(360^0-30^0)= \\ =- \frac{\sqrt3}{2} \\ \\ \\ y=sin195°cos195°= \frac{1}{2} 2 sin195°cos195°= \frac{1}{2} sin(2 195^0)= \frac{1}{2}sin390^0= \\ = \frac{1}{2}sin(360^0+30^0)= \frac{1}{2}sin30^0= \frac{1}{2} \frac{1}{2} = \frac{1}{4} \\ \\ \\ \frac{x}{ \sqrt{y} }=...}\)

[RAFAELLO14]

mozesz mi wytlumaczyc dlaczego \(\displaystyle{ sin ^{2}165°-cos ^{2} = -cos(2 165°)}\)...?

[wb]

\(\displaystyle{ cos(2\alpha)=cos^2\alpha-sin^2\alpha}\)

[RAFAELLO14]

....dzieki