Question

prove that Tan A (Tan60-A) (Tan+A)= Tan3A​

Answer 1

Answer:

Let us calculate tan (60 + A) and tan (60 – A).

tan(60+A)=tan600+tanA1–tan600tanA

⇒ tan(60+A)=3√+tanA1–3√tanA…………………….(1)

tan(60–A)=tan600−tanA1+tan600tanA

⇒ tan(60–A)=3√–tanA1+3√tanA……………………..(2

Subtracting equation (1) and (2)

tan(60+A)–tan(60–A)=3√+tanA1–3√tanA–3√–tanA1+3√tanA tan(60+A)–tan(60–A)=(3√+ta

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