Question

cho cos α=\(\dfrac{1}{3}\).khi đó giá trị biểu thức B=sin(α-\(\dfrac{\Pi}{4}\))-cos\(\left(\text{α}-\dfrac{\Pi}{4}\right)\)là bao nhiêu?

có ai bt làm ko giúp mik với

Answer 1

\(sin\left(\text{α}-\dfrac{\Pi}{4}\right)-cos\left(\text{α}-\dfrac{\Pi}{4}\right)\)

\(=sin\text{α}.cos\dfrac{\Pi}{4}-cos\text{α}-sin\dfrac{\Pi}{4}-\left(cos\text{α}.cos\dfrac{\Pi}{4}+sin\text{α}.sin\dfrac{\Pi}{4}\right)\)

\(=sin\text{α}.\dfrac{\sqrt{2}}{2}-\dfrac{1}{3}.\dfrac{\sqrt{2}}{2}-\dfrac{1}{3}.\dfrac{\sqrt{2}}{2}-sin\text{α}.\dfrac{\sqrt{2}}{2}\)

\(=\dfrac{-2\sqrt{2}}{6}\)

\(=\dfrac{-\sqrt{2}}{3}\)