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  4. The value of tan3A - tan2A - tanA is equal to

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Q. The value of $tan3A - tan2A - tanA$ is equal to

Trigonometric Functions

Solution:

$tan3A = tan\left(2A + A\right)$
$\Rightarrow tan3A=\frac{tan\,2A+tan\,A}{1-tan\,2A\,tan\,A}$
$\Rightarrow tan3A - tan3A \,tan2A\, tanA$
$ = tan2A + tanA$
$\Rightarrow tan3A - tan2A - tanA$
$ = tan3A\, tan2A\, tanA$