Question #13057

1 Answer
Narad T.
Nov 28, 2017

See the proof below

Explanation:

We need

#cottheta=costheta/sintheta#

#tantheta=sintheta/costheta#

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

Therefore,

#LHS=(1+cot^2theta)tan^2theta#

#=(1+cos^2theta/sin^2theta)*sin^2theta/cos^2theta#

#=(sin^2theta+cos^2theta)/cancel(sin^2theta)*cancel(sin^2theta)/cos^2theta#

#=1/cos^2theta#

#=sec^2theta#

#=RHS#

#QED#

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