Tính giá trị biểu thức sau \(\left(2\sin30^0+\cos135^0-3\tan150^0\right)\left(\cos180^0-\cos60^0\right)\)
\(-\dfrac{3}{2}\left(1-\dfrac{\sqrt{2}-2\sqrt{3}}{2}\right)\) \(\dfrac{\sqrt{2}+3\sqrt{3}}{2}\) \(\dfrac{\sqrt{2}-3\sqrt{3}}{2}\) \(\dfrac{1}{2}\) Hướng dẫn giải: Sử dụng \(\sin30^0=\dfrac{1}{2},\cos135^0=-\cos45^0=-\dfrac{\sqrt{2}}{2},\tan135^0=-\tan30^0=-\dfrac{1}{\sqrt{3}}\), \(\cos180^0=-1,\cos60^0=\dfrac{1}{2}\).
Suy ra \(\left(2\sin30^0+\cos135^0-3\tan150^0\right)\left(\cos180^0-\cos60^0\right)\)\(=-\dfrac{3}{2}\left(1-\dfrac{\sqrt{2}-2\sqrt{3}}{2}\right)\).
