Prove that {cotA/(cotA-cot3A)}-{tanA/(tan3A-tanA)}=1

Steps to prove {cotA/(cotA-cot3A)}-{tanA/(tan3A-tanA)}=1

L.H.S

={cotA/(cotA-cot3A)}-{tanA/(tan3A-tanA)}

={(1/tanA)/(1/tanA-1/tan3A)}-{tanA/(tan3A-tanA)}

=(1/tanA).(tan3A.tanA/tan3A-tanA)-tanA/(tan3A-tanA)

=tan3A/(tan3A-tanA)-tanA/(tan3A-tanA)

=(tan3A-tanA)/(tan3A-tanA)=1

=R.H.S

Hence {cotA/(cotA-cot3A)}-{tanA/(tan3A-tanA)}=1 is proved.

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