三角函数化简 化简sin 50(1+√3tan10)

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热心网友 时间：2023-07-16 05:06

三角函数化简 化简sin 50（1+√3tan10）

sin50°*(1+根号3×tan10°)
=sin50°*(1+根号3*sin10°/cos10°)
=sin50°/cos10°*(cos10°+根号3*sin10°)
=2*sin50°/cos10°*(1/2*cos10°+根号 3/2*sin10°)
=2*sin50°/cos10°*(sin30°*cos10°
+cos30°*sin10°)
=(2*sin50°/cos10°)* sin40°
=(2*cos40°/cos10°)* sin40°
=(2* sin40°cos40°)/ cos10°
=sin80°/cos10°
=cos10°/cos10°
=1

利用三角函数公式化简sin50度(1+√3tan10度)

=sin50°(1+sin60°sin10°/cos60°cos10°)
=sin50°(cos60°cos10°+sin60°sin10°)/cos60°cos10°
=sin50°(cos(60°-10°)/cos60°cos10°
=sin50°cos50°/(1/2cos10°)
=2sin50°cos50°/cos10°
=sin100°/cos10°
=cos10°/cos10°
=1

化简求值sin50°（1+√3tan10°）=？

原式=sin50(1+tan60tan10）
=sin50(1+sin60sin10/cos60cos10)
=sin50(cos60cos10+sin60sin10)/(cos60cos10)
=sin50cos(60-10)/(cos60cos10)
=2sin50cos50/(2cos60cos10)
=sin100/(2cos60cos10)
=sin(90+10)/(2cos60cos10)
=cos10/(2cos60cos10)
=1/(2cos60)
=1

化简[2sin50+sin10(1+√3tan10)] √(2sin^100°)

[2sin50+sin10(1+√3tan10)] √(2sin^100°)
=[2sin(60-10)+sin10+√3(sin10)^2/cos10]√(2sin^100°)
=[2*(√3/2cos10-1/2sin10)+sin10+√3(sin10)^2/cos10]√(2sin^100°)
=[√3cos10-sin10+sin10+√3(sin10)^2/cos10]√(2sin^100°)
=[(√3(cos10)^2+√3(sin10)^2)/cos10]√(2sin^100°)
=√3/cos10*√2cos10
=√6/√cos10
√(2sin^100°)是这样么？
你看啊有哪里错了 按常理化简出来是常数的吧

利用三角函数公式化简 sin50度（1+根号3 tan10度）

sin50（1+√3 tan10）
=sin50(tan60-tan10)/tan(60-10)
=sin50/tan50*(sin60/cos60-sin10/cos10)
=cos50*(sin60cos10-sin10cos60)/(cos60cos10)
=cos50*sin(60-10)/(cos60cos10)
=1/2sin100/(cos60cos10)
=sin80/cos10
=1

三角函数 tanθcosα+sinα化简

tanθcosα+sinα=√(1+tan²θ) *(sinαcosθ+cosαsinθ)=√(1+tan²θ) *sin(α+θ)

化简sin50°+cos40°(1+√3tan10°)/sin^270°

sin50+cos40(1+根号3tan10)/-1
=sin50+cos40[2*(sin30cos10+cos30sin10)/cos10]/-1
=sin50+cos40[2*sin40/cos10]/-1
=sin50+sin80/cos10)-1
=sin50-1
已用计算器演算

化简[2sin50°+sin10°(1+√3tan10°)] √(2sin280°)

[2sin50°+sin10°(1+√3tan10°)]•√(2sin²80°)
= [2sin50 + sin10(cos10+√3sin10)/cos10]•√2sin80
= [2sin50cos10+2sin10(cos60cos10+sin60sin10)•√2sin80/cos10
= 2[sin50cos10 + sin10cos(60-10)]•√2
= 2sin(50+10)•√2
= √6

sin50°（1+3tan10°）化简谢

sin50（1+√3tan10）
=sin50[1+√3(sin10/cos10)]
=sin50[(cos10+√3sin10)/cos10]
=2sin50[(1/2cos10+√3/2sin10)/cos10]
=sin50[2sin(30+10)/cos10]
=(2sin50sin40)/cos10°
=(2cos40°*sin40°)/cos10°
=sin80°/cos10°
=cos10°/cos10°
=1

化简cos50(1+根号3tan10

不知道你题出没出错啊。。。。
sin50(1+√3tan10)
=sin50(cos10+√3sin10)/cos10
=sin50*2sin(10+30)/cos10
=2sin50sin40/cos10
=2sin50cos50/cos10
=sin100/cos10
=sin80/cos10
=cos10/cos10
=1