求值:(tan1度*tan2度*tan3度*……*tan89度)/{(sin^2)1度+(sin^2)2度+(sin^2)3度+……+(sin^2)89度}

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求值:(tan1度*tan2度*tan3度*……*tan89度)/{(sin^2)1度+(sin^2)2度+(sin^2)3度+……+(sin^2)89度}求值:(tan1度*tan2度*tan3度*

求值:(tan1度*tan2度*tan3度*……*tan89度)/{(sin^2)1度+(sin^2)2度+(sin^2)3度+……+(sin^2)89度}
求值:(tan1度*tan2度*tan3度*……*tan89度)/{(sin^2)1度+(sin^2)2度+(sin^2)3度+……+(sin^2)89度}

求值:(tan1度*tan2度*tan3度*……*tan89度)/{(sin^2)1度+(sin^2)2度+(sin^2)3度+……+(sin^2)89度}
分子:
tan1度*tan2度*tan3度.tan87度* tan88度*tan89度
=tan1度*tan89度*tan2度* tan88度*tan3度*tan87度.(共45组)
=1×1×1×1.
=1
注意:tanα×tan(90°-α)=1
分母:
sin89=sin(90-1)=cos1
同理,sin88=cos2,in87=cos3,……,sin45=cos44
所以原式=[(sin1)^2+(cos1)^2]+[(sin2)^2+(cos2)^2]+……+[(sin44)^2+(cos44)^2]+(sin45)^2
=1+1+……+1+(根号2/2)^2
=44+1/2
=89/2
原式=1/(89/2)=2/89