Đáp án:
$\frac{\sqrt[]{10}-2\sqrt[]{2}}{6}$
Giải thích các bước giải:
$cos(α+\dfrac{π}{4})=cosα.cos\dfrac{π}{4}-sinα.sin\dfrac{π}{4}$
$sin^2α+cos^2α=1$
$⇒cos^2α=1-sin^2α$
$⇔cos^2α=1-\dfrac{2}{3}$
$⇔cos^2α=\dfrac{5}{9}$
$⇒cosα=\dfrac{\sqrt[]{5}}{3}$ do $(0<α<\dfrac{π}{2})$
$⇒cos(α+\dfrac{π}{4})=\dfrac{\sqrt[]{5}}{3}.cos\dfrac{π}{4}-\dfrac{2}{3}.sin\dfrac{π}{4}= \frac{\sqrt[]{10}-2\sqrt[]{2}}{6}$
