化简[2sin50+sin10(1+√3tan10)] √(1+cos20) 麻烦简单点,

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化简[2sin50+sin10(1+√3tan10)] √(1+cos20) 麻烦简单点,

化简[2sin50+sin10(1+√3tan10)] √(1+cos20) 麻烦简单点,
化简[2sin50+sin10(1+√3tan10)] √(1+cos20) 麻烦简单点,

化简[2sin50+sin10(1+√3tan10)] √(1+cos20) 麻烦简单点,
[2sin50°+sin10°(1+√3tan10°)] √(1+cos20°)
=[2sin50°+sin10°(1+√3sin10°/cos10°]√(1+2cos²10°-1)
=[2sin50°+sin10°(cos10°+√3sin10°)/cos10°]√(2cos²10°)
=[2sin50°+2sin10°(1/2cos10°+√3/2sin10°)/cos10°]√2cos10°
=[2sin50°+2sin10°sin(30°+10°)/cos10°]√2cos10°
=2√2cos10°[sin50°+sin10°sin40°/cos10°]
=2√2cos10°[sin50°cos10°+sin10°cos50°]/cos10°
=2√2sin(50°+10°)
=2√2sin60°
=2√2*(√3/2)
=√6