Mathematics Trigonometry Inverse Trigonometric Functions

What is \(\tan ^{-1}\left(\frac{a}{b}\right)-\tan ^{-1}\left(\frac{a-b}{a+b}\right)\) equal to?

1
\(-\frac{\pi}{4}\)
2
\(\frac{\pi}{4}\)
3
\(\tan ^{-1}\left(\frac{a^2-b^2}{a^2+b^2}\right)\)
4
\(\tan ^{-1}\left(\frac{2 a b}{a^2+b^2}\right)\)

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