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

  • \[\frac{\pi}{4}\]

     

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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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APPEARS IN

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