Evaluate tan-1(tan 9π/4)

We know that \( tan \dfrac{9\pi}{4}= 1\)

By substituting this value in \( tan^{-1}( tan \dfrac{9\pi}{4})\) we get,

Tan^-1 (1)

Now let tan^-1 (1) = y

Tan y = 1

\( tan \dfrac{\pi}{4} = 1\)

The range of the principal value of tan^-1 is \( (\dfrac{-\pi}{2},\dfrac{\pi}{2})\)

and  \( tan \dfrac{\pi}{4} = 1\)

Therefore \( tan^{-1}( tan \dfrac{9\pi}{4})=\)  \( \dfrac{\pi}{4} \)