Question

CM: (Sina - Cosa)² =\(\sqrt{2}\) Cos²(a+\(\dfrac{\pi}{4}\))

Answer 1

Có \(\sin a-\cos a=-\sqrt{2}\left(-\sin a.\sin\dfrac{\pi}{4}+\cos a.\cos\dfrac{\pi}{4}\right)\)

\(=-\sqrt{2}\cos\left(a+\dfrac{\pi}{4}\right)\)

\(\Rightarrow\left(\sin a-\cos a\right)^2=2.\cos^2\left(a+\dfrac{\pi}{4}\right)\)