已知sin(x+20°)=cos(x+10°)+cos(x-10°),则tanx=_.

问题描述:

已知sin(x+20°)=cos(x+10°)+cos(x-10°),则tanx=______.

∵sin(x+20°)=cos(x+10°)+cos(x-10°),∴sinxcos20°+cosxsin20°=2cosxcos10°,∴tanx=2cos10°−sin20°cos20°=2cos(30°−20°)−sin20°cos20°=2cos30°cos20°+2sin30°sin20°−sin20°cos20°=2c...