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Question
The value of tan3A - tan2A - tanA is equal to ______.
Options
tan3A tan2A tanA
-tan3A tan2A tanA
tanA tan2A - tan2A tan3A - tan3A tanA
None of these
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Solution
The value of tan 3A - tan 2A - tan A is equal to tan3A tan2A tanA.
Explanation:
tan3A tan2A tanA
The given expression is tan3A - tan2A - tanA
tan3A = tan(2A + A)
⇒ tan3A = `(tan2"A" + tan"A")/(1 - tan2"A" tan"A")`
⇒ tan3A(1 - tan2A tanA) = tan2A + tanA
⇒ tan3A - tan3A tan2A tanA = tan2A + tanA
⇒ tan3A - tan2A - tanA = tan3A tan2A tanA
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