化简[2sin50°+sin10°(1+3tan10°)]1+cos20°．

Question

化简[2sin50°+sin10°(1+√(3)tan10°)]√(1+cos20°)．

Answer 1

原式=[2sin50°+sin10°（1+(√(3)sin10°)/(cos10°)）]√(1+cos20°)
=（2sin50°+sin10°•(cos10°+√(3)sin10°)/(cos10°)）√(1+cos20°)
=（2sin50°+2sin10°•(sin(10°+30°))/(cos10°)）√(1+cos20°)
=(2sin50°cos10°+2sin10°sin40°)/(cos10°)•√(1+cos20°)
=2cos（40°-10°）•(√(2)cos10°)/(cos10°)
=2cos30°×√(2)
=√(6)．