Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# If Tan θ = 1 2 and Tan ϕ = 1 3 , Then the Value of Tan ϕ = 1 3 is - Mathematics

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

• $\frac{\pi}{4}$

#### 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.

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 7 Values of Trigonometric function at sum or difference of angles
Q 15 | Page 28