Quick Help with Tangent Sum Formula: Solving for Tan 15 and Tan 30

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SUMMARY

The discussion revolves around the Tangent sum formula, specifically for calculating Tan(15) and Tan(30). The correct application of the formula Tan(a+b) = (Tan a + Tan b) / (1 - Tan a * Tan b) leads to the conclusion that Tan(15 + 30) equals Tan(45), which is 1. The initial confusion stemmed from a misinterpretation of the formula and a potential misprint in the study material, which incorrectly suggested the answer was -1.

PREREQUISITES
  • Understanding of trigonometric identities, particularly the Tangent sum formula.
  • Familiarity with exact values of tangent for common angles (e.g., Tan(15), Tan(30), Tan(45)).
  • Basic algebra skills for manipulating fractions and equations.
  • Knowledge of how to express angles in radians and degrees.
NEXT STEPS
  • Study the derivation and applications of the Tangent sum formula in trigonometry.
  • Learn how to calculate exact values of tangent for other angles, such as Tan(45) and Tan(60).
  • Explore related trigonometric identities, such as the Sine and Cosine sum formulas.
  • Practice solving problems involving tangent and other trigonometric functions to reinforce understanding.
USEFUL FOR

Students preparing for pre-calculus exams, educators teaching trigonometry, and anyone seeking to deepen their understanding of trigonometric identities and their applications.

CINA
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Hi, I'm studying for my pre-calc test tomorrow and I've run into a snag. I just can't seem to get the correct answer for a Tangent sum problem, and I'm hoping someone could help me out with it. It goes like this:

Sum Formula for Tangant: Tan (a+b) = Tan a + Tan b/1-Tan a * Tan b

Problem: Find the exact value,
Tan 15 + Tan 30/1- Tan 15 * Tan 30

Correct answer: -1

but I can't seem to get the answer in the end; are the tangants in the numerator added to make tan 45 then solved for? If not, how would you express tan 15 in an exact form? Similarly, how do you multiply tan 15 and tan 30? Or am I missing some other identity?

Its been driving me crazy all day!:cry:
 
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(Tan 15 + Tan 30) / (1- Tan 15 * Tan 30) =
Tan(15+30) =
Tan(45) =
1

The answer you have is wrong.
 
I don't think that's the correct answer. It should be 1. Just apply the formula backwards to get it.
 
Huh, that's quite odd... misprint in the book I suppose. Heh, it makes more sense now, thanks!
 

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