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If tanθ

Question:

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

(a) $\frac{\pi}{6}$

(b) $\pi$

(c) 0

(d) $\frac{\pi}{4}$

Solution:

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

Now,

$\tan (\theta+\phi)=\frac{\tan \theta+\tan \phi}{1-\tan \theta \tan \phi}$

$=\frac{\frac{1}{2}+\frac{1}{3}}{1-\frac{1}{2} \times \frac{1}{3}}$

$=\frac{\frac{5}{6}}{\frac{5}{6}}$

= 1

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

Hence, the correct answer is option D.

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