Choose all the ones that are equal tan-- tan15151+ tan-tan1515O 13/3O tan()tan()3O tan()3tan(5)tan()tan30

Giventan7π15−tan2π151+tan7π15tan2π15

Answered: tan- tan 15 15 1+ tan tan 15 15 O V3 O…

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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Question

Choose all the ones that are equal

tan-
- tan
15
15
1+ tan-
tan
15
15
O 13
/3
O tan()
tan()
3
O tan()
3
tan(5)
tan()
tan
30

Expert Solution

Step 1

$\begin{array}{l} Given \\ \frac{\tan \frac{7 π}{15} - \tan \frac{2 π}{15}}{1 + \tan \frac{7 π}{15} \tan \frac{2 π}{15}} \end{array}$

Step 2

$\begin{array}{l} Using Formula \\ tan (A - B) = \frac{\tan A - \tan B}{1 + \tan A \tan B} \\ Here \\ A= \frac{7 π}{15}, B= \frac{2 π}{15} \\ \frac{\tan \frac{7 π}{15} - \tan \frac{2 π}{15}}{1 + \tan \frac{7 π}{15} \tan \frac{2 π}{15}} = \tan (\frac{7 π}{15} - \frac{2 π}{15}) \\ \frac{\tan \frac{7 π}{15} - \tan \frac{2 π}{15}}{1 + \tan \frac{7 π}{15} \tan \frac{2 π}{15}} = \tan (\frac{7 π - 2 π}{15}) \\ \frac{\tan \frac{7 π}{15} - \tan \frac{2 π}{15}}{1 + \tan \frac{7 π}{15} \tan \frac{2 π}{15}} = \tan (\frac{5 π}{15}) \\ \frac{\tan \frac{7 π}{15} - \tan \frac{2 π}{15}}{1 + \tan \frac{7 π}{15} \tan \frac{2 π}{15}} = \tan (\frac{π}{3}) \\ \frac{\tan \frac{7 π}{15} - \tan \frac{2 π}{15}}{1 + \tan \frac{7 π}{15} \tan \frac{2 π}{15}} = \sqrt{3} \end{array}$

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