Question #562b9

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Answer 1 · 2016-12-03T06:19:30

To prove #1+tanxtan2x=tan2xcotx-1#

#LHS=1+tanxtan2x#

#=1+(tanx xx2tanx)/(1-tan^2x)#

#=(1-tan^2+2tan^2x)/(1-tan^2x)#

#=(1+tan^2x)/(1-tan^2x)#

#=(2-1+tan^2x)/(1-tan^2x)#

#=(2-(1-tan^2x))/(1-tan^2x)#

#=2/(1-tan^2x)-(1-tan^2x)/(1-tan^2x)#

#=(2tanxcotx)/(1-tan^2x)-1#

#=tan2xcotx-1=RHS#

Proved