Question

tan13A - tan7A - tan6A = tan13A tan7A tan6A

Answer 1

Answer :

We know that,

tan(A - B) = (tanA - tanB)/(1 + tanA tanB)

⇒ tanA - tanB = (1 + tanA tanB) tan(A - B)

Now,

L.H.S. = tan13A - tan7A - tan6A

= (tan13A - tan7A) - tan6A

= (1 + tan13A tan7A) tan(13A - 7A) - tan6A,

using the above formula

= (1 + tan13A tan7A) tan6A - tan6A

= tan6A + tan13A tan7A tan6A - tan6A

= tan13A tan7A tan6A

= R.H.S. [Proved]

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