Prove that cot3A=(cot^3A-3cotA)/(3cot^2A-1)

Steps to prove cot3A=(cot^3A-3cotA)/(3cot^2A-1)

L.H.S

=cot3A

=cot(2A+A)

=(cot2A.cotA-1)/(cotA+cot2A)

={((cot^2A-1)/2cotA).cotA-1}/{cotA+(cot^2A-1)/2cotA)}

={(cot^3A-cotA-2cotA)/2cotA}/{(2cot^2A+cot^2A-1)/cot2A}

=(3cot^3A-3cotA)/(3cot^2A-1)

=R.H.S

Hence cot3A=(cot^3A-3cotA)/(3cot^2A-1) is proved.

Detail Information:-

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