若tan(θ+π/4)=2,则tan(2θ+π/4)等于?求详细过程!
问题描述：
若tan(θ+π/4)=2,则tan(2θ+π/4)等于?
求详细过程!
答
tan(θ+π/4)=(tanθ+tanπ/4)/(1-tanθtanπ/4)=(tanθ+1)/(1-tanθ)=2
解得：tanθ=1/3
tan2θ=3/4
tan(2θ+π/4)=7
答
结果是7 过程打太费劲了。。。0 0
答
tan(θ+π/4)=[tanθ+tan(π/4)]/[1-tanθtan(π/4)]=(tanθ+1)/(1-tanθ)=2即tanθ+1=2(1-tanθ)解得：tanθ=1/3 tan(2θ+π/4)=tan[θ+(θ+π/4)]=[tanθ+tan(θ+π/4)]/[1-tanθtan(θ+π/4)]=(1/3+2)/[1-(1/3)*2...
答
tanπ/4=1
所以tan(θ+π/4)=2
则(tanθ+1)/(1-tanθ)=2
解得tanθ=1/3
所以tan2θ=2tanθ/(1-tan²θ)=3/4
所以原式=(tan2θ+1)/(1-tan2θ)=7