Question

tan5A- tan3A- tan2A = tan5A× tan3A×tan2A​

Answer 1

Let,

➡ 5A = 2A + 3A

5A = 2A + 3ATake tan of both sides

➡ tan(5A) = tan(2A) + tan(3A).........(eq1)

tan(5A) = tan(2A) + tan(3A).........(eq1)we know that,

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

Tan(A+B) = (Tan A + Tan B)/(1-Tan A Tan B)we get

➡ Tan (5A) = (Tan 3A + Tan 2A)/(1- Tan 3A TAN 2A)

➡ Tan 5A(1-Tan 3A Tan 2A) = tan 3A +tan 2A

➡ Tan 5A -Tan 5A Tan 3A Tan 2A = Tan 3A +tan 2A

➡ Tan 5A - Tan 3A - Tan 2A = Tan 5A.Tan 3A Tan 2A

Hence it is proved ....

Step-by-step explanation:

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