tan(π/8)-cot(π/8)的值为

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tan(π/8)-cot(π/8)的值为

tan(π/8)-cot(π/8)的值为
tan(π/8)-cot(π/8)的值为

tan(π/8)-cot(π/8)的值为
【参考答案】-2
原式=tan(π/8)-cot(π/8)
=[sin(π/8)/cos(π/8)]-[cos(π/8)/sin(π/8)]
={sin²(π/8)/[sin(π/8)cos(π/8)]}-{cos²(π/8)/[sin(π/8)cos(π/8)]}
=[sin²(π/8)-cos²(π/8)]/[sin(π/8)cos(π/8)]
=-cos(π/4)/[(1/2)sin(π/4)]
=-2

tan(π/8)-cot(π/8)=1/2

tan(π/8)-cot(π/8)的值为?
tan(π/8)-cot(π/8)=sin(π/8)/cos(π/8)-cos(π/8)/sin(π/8)
=[sin²(π/8)-cos²(π/8)]/[sin(π/8)cos(π/8)]
=-cos(π/4)/[(1/2)sin(π/4)]=-2cot(π/4)=-2

tan(π/8)-cot(π/8)=sin(π/8)/cos(π/8)-cos(π/8)/sin(π/8)
=[sin²(π/8)-cos²(π/8)]/sin(π/8)cos(π/8)
=-2cos(π/4)/sin(π/4)
=-2

=-(1-tan(π/8)*2/tan(π/8)=-2/tan(π/4)=-2