How to prove cot x + tan 2x=cot x sec2x?

1 Answer
Narad T.
Dec 23, 2017

See the proof below

Explanation:

Reminder :

#cotx=cosx/sinx#

#tanx=sinx/cosx#

#cos(a-b)=cosacosb+sinasinb#

#secx=1/cosx#

Therefore,

#LHS=cosx+tan2x#

#=cosx/sinx+(sin2x)/(cos2x)#

#=(cosxcos2x+sinxsin2x)/(sinxcos2x)#

#=(cosx)/(sinxcos2x)#

#=cosx/sinx*1/(cos2x)#

#=cotxsec2x#

#=RHS#

#QED#

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