Question

The value of tan 3A – tan 2A – tan A is equal to
(A) tan 3A tan 2A tan A (B) – tan 3A tan 2A tan A 
(C) tan A tan 2A – tan 2A tan 3A – tan 3A tan A (D) None of these

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Answer 1

Explanation:

We can write

tan(3A) = tan(2A + A)

We have the formula

tan(X + Y) = [ tan(X) + tan(Y) ] / [1 - tan(X).tan(Y) ]

Applying this we get

tan(3A) = [ tan(2A) + tan(A) ] / [1 - tan(2A).tan(A) ]

tan(3A) [ 1 - tan(2A).tan(A) ] = tan(2A) + tan(A)

Solving this we get

tan(3A) - tan(A).tan(2A).tan(3A) = tan(2A) + tan(A)

So,

tan(3A) - tan(2A) - tan(A) = tan(A).tan(2A).tan(3A)

Therefore, option A is correct.

Answer 2

Answer:

l

(B) – tan 3A tan 2A tan A