Question

derive the formula for cot 3A​

Answer 1

Answer:

Cot3A = Cot(2A + A)

Cot3A = 1/Tan (2A + A)

In terms of Tan:

Cot3A = 1/{(Tan2A +TanA)/(1— Tan2A.TanA)}

Cot3A = (1—Tan2A.TanA)/(Tan2A + TanA)

AND

In terms of Cot:

Cot3A = {1—(1/Cot2A).(1/CotA)}/{(1/Cot2A)+(1/CotA)}

Cot3A = {(Cot2A.CotA—1)/(Cot2A.CotA)}/{(CotA+Cot2A)/(Cot2A.CotA)}

Cot3A = Cot2A.CotA—1/Cot2A+ CotA