\tan 3A-\tan 2A-\tan A is equal to

  • Option 1)

    -tan 3A \tan 2A \tan A

  • Option 2)

    \tan A \tan 2A \tan 3A

  • Option 3)

    \tan A \tan 2A - \tan 2A \tan 3A - \tan 3A \tan A

  • Option 4)

    None of these

 

Answers (1)
V Vakul

As learnt in

Triple Angle Formula -

Triple angle formula

- wherein

These are formulae for triple angles.

 

 

Double Angle Formula -

Double angle formula

- wherein

These are formulae for double angles.

 

 \tan 3A - \tan 2A- \tan A

= \frac{3\tan A- \tan ^{3}A}{1 - 3\tan ^{2}A} - \frac{2\tan A}{1 - \tan ^{2}A} - \tan A

\Rightarrow \tan A \left [ \frac{3- \tan ^{2}A}{1 - 3\tan ^{2}A} - \frac{2}{1 - \tan ^{2}A} - 1\right ]                     \\ \left [ \because \tan 3A = \frac{3\tan A - \tan ^{3}A}{1 - 3\tan ^{2}A} \ and\ \tan 2A = \frac{2\tan A}{1 - \tan ^{2}A} \right ]

\Rightarrow \tan A \left [ \frac{3- \tan ^{2}A}{1 - 3\tan ^{2}A} - \frac{3- \tan ^{2}A}{1- \tan ^{2}A}\right ]

\Rightarrow \left ( tanA \right )\left ( 3 - \tan ^{2}A \right )\left [ \frac{1 - \tan ^{2}A-1+3\tan ^{2}A}{\left ( 1 - 3\tan ^{2}A \right )\left ( 1 - \tan ^{2}A \right )} \right ]

\Rightarrow \frac{\left ( \tan A \right )\left ( 3-\tan ^{2}A \right )\left ( 2\tan ^{2}A \right )}{\left ( 1 - 3\tan ^{2}A\right )\left ( 1 - \tan ^{2}A \right )}

\Rightarrow \frac{2\tan A}{\left ( 1 - \tan ^{2}A \right )}\times \tan A\times \frac{3\tan A - \tan ^{3}A}{1 - 3\tan ^{2}A}

\Rightarrow \tan 2A\times \tan A\times \tan 3A

\Rightarrow \tan A \ \tan 2A \ \tan 3A


Option 1)

-tan 3A \tan 2A \tan A

This option is incorrect

Option 2)

\tan A \tan 2A \tan 3A

This option is correct

Option 3)

\tan A \tan 2A - \tan 2A \tan 3A - \tan 3A \tan A

This option is incorrect

Option 4)

None of these

This option is incorrect

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