How do you prove #(tan(x)-1)/(tan(x)+1)= (1-cot(x))/(1+cot(x))#?

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Answer 1 · 2015-04-19T20:14:42

Start off by cross multiplying

#(tanx-1)(1+cotx)=(tanx+1)(1-cotx)#

Expand each side using FOIL

#tanx+tanxcotx-1-cotx#
#=tanx-tanxcotx+1-cotx#

Since #tanx# and #cotx# are reciprocals

#tanxcotx=1#

Now we can write

#tanx+1-1-cotx=tanx-1+1-cotx#

Simplifying each side

#tanx-cotx=tanx-cotx#

The right hand side and left hand side are the same

Answer 2 · 2015-04-19T21:21:50

Apr 19, 2015

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