Question #b30b0

1 Answer
Narad T.
Feb 12, 2018

See the explanation below

Explanation:

We need

#cos^2x+sin^2x=1#

#tanx=sinx/cosx#

#cotx=cosx/sinx#

Therefore,

#(tanx-cotx)/(tanx+cotx)+2cos^2x#

#=(sinx/cosx-cosx/sinx)/(sinx/cosx+cosx/sinx)+2cos^2x#

#=((sin^2x-cos^2x)/cancel(sinxcosx))/((sin^2x+cos^2x)/cancel(sinxcosx))+2cos^2x#

#=sin^2x-cos^2x+2cos^2x#

#=sin^2x+cos^2x#

#=1#

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