简单三角函数1.化简 sin^2(x-π/6) + sin^2(x+π/6) - sin^2x .2.求:sin50°*(1+√3tan10°)的值.

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简单三角函数1.化简 sin^2(x-π/6) + sin^2(x+π/6) - sin^2x .2.求:sin50°*(1+√3tan10°)的值.

简单三角函数1.化简 sin^2(x-π/6) + sin^2(x+π/6) - sin^2x .2.求:sin50°*(1+√3tan10°)的值.
简单三角函数
1.化简 sin^2(x-π/6) + sin^2(x+π/6) - sin^2x .
2.求:sin50°*(1+√3tan10°)的值.

简单三角函数1.化简 sin^2(x-π/6) + sin^2(x+π/6) - sin^2x .2.求:sin50°*(1+√3tan10°)的值.
1、原式=sin^2(x-π/6) + 2sin(x-π/6)sin(x+π/6)+sin^2(x+π/6)-2sin(x-π/6)sin(x+π/6) - sin^2x=[sin(x-π/6)+sin(x+π/6)]^2-2sin(x-π/6)sin(x+π/6)-sin^2x=[2sinxcosπ/6]^2-2sin(x-π/6)sin(x+π/6)-sin^2x=2sin^2x-2sin(x-π/6)sin(x+π/6)=2sin^2x-(-sinx+sinπ/6)=2sin^2x+sinx-1/2
2、原式=sin50°*[2/cos10°(1/2cos10°+√3/2sin10°)]=sin50°*[2/cos10°(sin30°cos10°+cos30°sin10°)]=sin50°*[2/cos10°(sin40°)]=sin50°*[2/cos10°(cos50°)]=2*sin50°cos50°/cos10°=sin100°/cos10°=cos(100°-90°)/cos10°=cos10°/cos10°=1