求sin^2(x)+tan^2(x)+csc^2(x)+sec^2(x)+cos^2(x)+cot^2(x)=31里,x的解法

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求sin^2(x)+tan^2(x)+csc^2(x)+sec^2(x)+cos^2(x)+cot^2(x)=31里,x的解法
求sin^2(x)+tan^2(x)+csc^2(x)+sec^2(x)+cos^2(x)+cot^2(x)=31里,x的解法

求sin^2(x)+tan^2(x)+csc^2(x)+sec^2(x)+cos^2(x)+cot^2(x)=31里,x的解法
sin^2(x)+tan^2(x)+csc^2(x)+sec^2(x)+cos^2(x)+cot^2(x)=31
得cos^2(x)+sin^2(x)+tan^2(x)+csc^2(x)+sec^2(x)+cot^2(x)=31
得1+tan^2(x)+csc^2(x)+sec^2(x)+cot^2(x)=31
即tan^2(x)+csc^2(x)+sec^2(x)+cot^2(x)=30
得sin²x/cos²x+1/sin²x+1/cos²x+cos²x/sin²x=30
得(1-cos²x)/cos²x+1/sin²x+1/cos²x+(1-sin²x)/sin²x=30
得1/cos²x-1+1/sin²x+1/cos²x+1/sin²x-1=30
得2/cos²x+2/sin²x=32
得1/cos²x+1/sin²x=16
得（cos²x+sin²x）/sin²xcos²x=16
得sin²xcos²x=1/16
得1/4sin²2x=1/16
得sin²2x=1/4
则sin2x=±1/2
所以2x=±π/6+2kπ或±5π/6+2kπ
则x=±π/12+kπ或±5π/12+kπ
和在一起写就是x=±π/12+kπ/2

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