Question

prove that,tan3A-tan2A-tanA=tan3A.tan2A.tanA

Answer 1

Step-by-step explanation:

We know that,

3A = 2A + A

Now, we also know,

Tan(A + B) = (Tan A + Tan B)/(1 - Tan A•Tan B)

Now,

Putting 2A and A instead of A and B respectively, we get,

Tan(2A + A) = (Tan 2A + Tan A)/(1 - Tan 2A•Tan A)

Tan 3A = (Tan 2A + Tan A)/(1 - Tan 2A•Tan A)

(Tan 2A + Tan A) = Tan 3A × (1 - Tan 2A•Tan A)

Tan 2A + Tan A = Tan 3A - Tan 3A•Tan 2A•Tan A

Tan 3A - Tan 2A - Tan A = Tan 3A•Tan 2A•Tan A

Hence proved.

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