Question

Tinh : A=(sin40+cos10)² -(cos40+sin10)² +cos140

Answer 1

A=sin²40+cos²10+2sin40cos10-cos²40-sin²10-2sin10cos40+cos(90+50)

A=(sin²40-cos²40)+(cos²10-sin²10)+2(sin40cos10-cos40sin10)-sin50

A=(sin40-cos40)(sin40+cos40)-(sin10-cos10)(sin10+cos10)+1-sin50

A=\(\sqrt{2}\) sin(40-\(\frac{\pi}{4}\))\(\sqrt{2}\) cos(40-\(\frac{\pi}{4}\))-\(\sqrt{2}\)sin(10-\(\frac{\pi}{4}\))\(\sqrt{2}\) cos(10-\(\frac{\pi}{4}\))+1-sin50

A=-2sin5cos5+2sin35cos35+1-sin50

A= - sin10+sin70+1-sin50

A= 2cos40sin30-sin(90-40)+1

A=cos40-cos40+1 =1