Question

求值:2sin50°+cos10°(1+根号3tan10°)/根号下1+2sin50°cos50°

Answer 1

2sin50°+cos10°(1+根号3tan10°)/纤斗根号下链族1+2sin50°cos50°
=(2sin50°+cos10°(1+√3*tan10°))/√毁唤磨(sin^2 50°+2sin50°cos50°+cos^2 50°)
=(2sin50°+cos10°+√3sin10°)/√√(sin50°+cos50°)^2
=(2sin50°+2sin(10°+30°))/(sin50°+cos50°)
=2(sin50°+sin40°)/(sin50°+cos50°)
=2(sin50°+cos50°)/(sin50°+cos50°)
=2

追问

2(sin50°+sin40°)/(sin50°+cos50°)
这一步怎么来的？没看懂！

追答

cos10°+√3sin10°
=2(1/2cos10°+√3/2sin10°)
=2(sin30°cos10°+cos30°sin10°)
=2sin(30°+10°)
=2sin40°