Question

[2sin50+sin10(1+√3*tan10)]√(1+cos20)

求一下

Answer 1

原式=[2sin(60°-10°)+sin10°(1+√3tan10°)]×√(1+cos20°)

=(√3cos10°-sin10°+sin10°+√3sin10°tan10°)×√(2cos²10°)

=√3(cos10°+sin10°tan10°)×√2cos10°

=√6(cos²10°+sin10°tan10°×cos10°)

=√6(cos²10°+sin²10°)

=√6

Answer 2

sin80°(1＋(√3)tan10°)=cos10(1＋(√3)tan10°) =2(cos10/2+√3/2sin10)=2sin40 [2sin50°＋sin80°(1＋(√3)tan10°)]x√（1+cos20°=2√2(sin50+sin40) cos10=2√2(sin50+cos50) cos10=4sin95cos10=4cos5 cos10