Question

. If the value of tan 3A =1 , the value of A is​

Answer 1

Answer:

Trigonometric function of tan 3A in terms of tan A is also known as one of the double angle formula.

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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