求f(x)=ln((sinx+cosx)/(sinx-cosx))的单调递减区间最好能有过程,谢.ln(1+tanxtanπ/4)/(tanx-tanπ/4) =lncot(x-π/4)这步怎么得到的?

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求f(x)=ln((sinx+cosx)/(sinx-cosx))的单调递减区间最好能有过程,谢.ln(1+tanxtanπ/4)/(tanx-tanπ/4) =lncot(x-π/4)这步怎么得到的?

求f(x)=ln((sinx+cosx)/(sinx-cosx))的单调递减区间最好能有过程,谢.ln(1+tanxtanπ/4)/(tanx-tanπ/4) =lncot(x-π/4)这步怎么得到的?
求f(x)=ln((sinx+cosx)/(sinx-cosx))的单调递减区间
最好能有过程,谢.
ln(1+tanxtanπ/4)/(tanx-tanπ/4) =lncot(x-π/4)
这步怎么得到的?

求f(x)=ln((sinx+cosx)/(sinx-cosx))的单调递减区间最好能有过程,谢.ln(1+tanxtanπ/4)/(tanx-tanπ/4) =lncot(x-π/4)这步怎么得到的?
f(x)=ln((sinx+cosx)/(sinx-cosx))
=ln(cosx(tanx+1)/cosx(tanx-1))
=ln(tanx+1)/(tanx-1)
=ln(1+tanxtanπ/4)/(tanx-tanπ/4)
=lncot(x-π/4)
因为cot是减函数,而ln却是增函数,所以f(x)在定义内是减函数
则有 cot(x-π/4)>0
kπ+π/2