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Prove that:

Question:

Prove that:

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

Solution:

To Prove: $\tan ^{-1} 2-\tan ^{-1} 1=\tan ^{-1} \frac{1}{3}$

Formula Used: $\tan ^{-1} x-\tan ^{-1} y=\tan ^{-1}\left(\frac{x-y}{1+x y}\right)$ where $x y>-1$

Proof:

$\mathrm{LHS}=\tan ^{-1} 2-\tan ^{-1} 1$

$=\tan ^{-1}\left(\frac{2-1}{1+2}\right)$

$=\tan ^{-1}\left(\frac{1}{3}\right)$

$=\mathrm{RHS}$

Therefore LHS = RHS

Hence proved.

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