数学高一下红对勾问题求值：tan
tan70 + cos10*(√3 tan20-1)
= sin70/cos70 + cos10(√3 sin20/cos20-1))
= sin70/cos70 + 2*cos10((√3/2) sin20-(1/2)cos20))/cos20
= sin70/cos70 + 2cos10sin(20-30)/cos20
= sin70/cos70 -sin20/cos20
= (sin70cos20 - cos70sin20)/(cos70cos20)
= sin50/((cos(70-20)+cos(70+20))/2)
= 2*sin50/cos50
= 2tan50
。 全部
tan70 + cos10*(√3 tan20-1)
= sin70/cos70 + cos10(√3 sin20/cos20-1))
= sin70/cos70 + 2*cos10((√3/2) sin20-(1/2)cos20))/cos20
= sin70/cos70 + 2cos10sin(20-30)/cos20
= sin70/cos70 -sin20/cos20
= (sin70cos20 - cos70sin20)/(cos70cos20)
= sin50/((cos(70-20)+cos(70+20))/2)
= 2*sin50/cos50
= 2tan50
。
收起
