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tan 3A in Terms of A

We will learn how to express the multiple angle of tan 3A in terms of A or tan 3A in terms of tan A.

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 = 3tanAtan3A13tan2A


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

Proof: tan 3A

= tan (2A + A)

= tan2A+tanA1tan2AtanA

= 2tanA1tan2A+tanA12tanA1tan2AtanA

= 2tanA+tanAtan3A1tan2A2tan2A

= 3tanAtan3A13tan2A

Therefore, tan 3A = 3tanAtan3A13tan2A

Note:

(i) In the above formula we should note that the angle on the R.H.S. of the formula is one-third of the angle on L.H.S. Therefore, tan 30° = 3tan10°tan310°13tan210°.

(ii) The value of tan 3A can also be obtain by putting A = B = C in the formula

tan (A + B + C) = tanA+tanB+tanCtanAtanBtanC1tanAtanBtanBtanCtanCtanA


 Multiple Angles




11 and 12 Grade Math 

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