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