- 化简求值√3sin50°(1+√3tan10°)
- √3sin50°(1+√3tan10°)
- sin50°(1+√3tan10°)
=sin(60°-10°)(1+√3tan10°)
=(√3cos10°-sin10°)(1+√3tan10°)/2
=[√3cos10°-sin10°+3sin10°-√3(sin10°)^2/cos10°]/2
=[√3(cos10°)^2-√3(sin10°)^2+2sin10°cos10°]/2cos10°
=(√3cos20°+sin20°)/2cos10°
=(cos30°cos20°+sin30°sin20°)/cos10°
=[cos(30°-20°)]/cos10°
=cos10°/cos10°=1
所以√3sin50°(1+√3tan10°=√3