MCQ

If \[\tan\theta = \frac{1}{2}\] and \[\tan\phi = \frac{1}{3}\], then the value of \[\tan\phi = \frac{1}{3}\] is

#### Options

- \[\frac{\pi}{6}\]
- \[\pi\]
0

- \[\frac{\pi}{4}\]

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#### Solution

It is given that \[\tan\theta = \frac{1}{2}\] and \[\tan\phi = \frac{1}{3}\]

Now,

\[\tan\left( \theta + \phi \right) = \frac{\tan\theta + \tan\phi}{1 - \tan\theta\tan\phi}\]

\[ = \frac{\frac{1}{2} + \frac{1}{3}}{1 - \frac{1}{2} \times \frac{1}{3}}\]

\[ = \frac{\frac{5}{6}}{\frac{5}{6}}\]

\[ = 1\]

\[\therefore \theta + \phi = \frac{\pi}{4} \left( \tan\frac{\pi}{4} = 1 \right)\]

Hence, the correct answer is option D.

Is there an error in this question or solution?

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