三角方程
已知x为锐再,试解方程 sin(x+20°)=cos(x+10°)+cos(x-10°).
解: sin(x+20°)=cos(x+10°)+cos(x-10°) →tanx=(2cos10°-sin20°)/cos20° =(cos10°+sin80°-sin20°)/cos20° =(cos10°+2cos50°sin30°)cos20° =(2cos30°cos20°)/cos20° =2cos30° =√3, ∴x=60°.
sinxcos20+cosxsin20=2cosxcos10 sinxcos20=cosx(2cos10-sin20) sinx/cosx=(2cos10-sin20)/cos20 tanx=(2cos10-sin20)/cos20=2cos10(1-sin10)/cos20 x=arctan(2cos10(1-sin10)/cos20)
答:1+9-x/1+9x=3 10-x=3+27x 28x=7 x=0.25(1/4)详情>>
答:详情>>