How do you prove #(1+tanx)/(1+cotx)=2#?

2 Answers
May 24, 2016

This identity is false!!!

Explanation:

Simplifying the left side:

#(1 + sinx/cosx)/(1 + cosx/sinx)

#((cosx + sinx)/cosx)/((sinx + cosx)/sinx) #

#(cosx + sinx)/cosx xx sinx/(sinx + cosx) = #

#sinx/cosx#

#tanx#

Hopefully this helps!

May 24, 2016

Another way to prove this false is as follows.

Since #(tanx)/(tanx) = 1# and #tanxcotx = tanx*1/(tanx) = 1#:

#color(blue)((1+tanx)/(1+cotx))*(tanx)/(tanx)#

#= (tanx(1+tanx))/(tanx + tanxcotx)#

#= (tanxcancel((1+tanx)))/cancel(1+tanx)#

#= color(blue)(tanx)#