Question

what is the formula of tan3A with full derivation

Answer 1

If A is a number or angle then we have, tan 3A = 3tanA−tan3A1−3tan2A

Now we will proof the above multiple angle formula step-by-step.

Proof: tan 3A

= tan (2A + A)

= tan2A+tanA1−tan2A⋅tanA

= 2tanA1−tan2A+tanA1−2tanA1−tan2A⋅tanA

= 2tanA+tanA−tan3A1−tan2A−2tan2A

= 3tanA−tan3A1−3tan2A

Therefore, tan 3A = 3tanA−tan3A1−3tan2A

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Answer 2

Answer:

The derivation is in the attachment.

Also, tan3A = 3tanA - tan^3A/1-3tan^2 A