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

In summary, the conversation is about a pre-calc student seeking help with a Tangent sum problem. The problem is to find the exact value of Tan 15 + Tan 30 divided by 1- Tan 15 multiplied by Tan 30. The correct answer is -1 and the correct method is to apply the formula for Tangant sum in reverse. The student realizes there was a misprint in the book and thanks the person for their help.
  • #1
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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  • #2
(Tan 15 + Tan 30) / (1- Tan 15 * Tan 30) =
Tan(15+30) =
Tan(45) =
1

The answer you have is wrong.
 
  • #3
I don't think that's the correct answer. It should be 1. Just apply the formula backwards to get it.
 
  • #4
Huh, that's quite odd... misprint in the book I suppose. Heh, it makes more sense now, thanks!
 

1. What is the tangent sum formula?

The tangent sum formula is a mathematical identity that expresses the sum of two tangents in terms of their difference. It is written as tan(A+B) = (tanA + tanB) / (1 - tanAtanB), where A and B are angles.

2. How is the tangent sum formula used?

The tangent sum formula is used to simplify trigonometric expressions involving sums of tangents. It can also be used to find the tangent of a sum of angles, given the tangents of the individual angles.

3. What is the derivation of the tangent sum formula?

The tangent sum formula can be derived using the double angle formula for tangent, along with the addition and subtraction formulas for tangent. It can also be derived from the Pythagorean identity for tangent.

4. Are there any special cases for the tangent sum formula?

Yes, there are two special cases for the tangent sum formula. When A and B are complementary angles, the formula becomes tan(A+B) = 1. When A and B are supplementary angles, the formula becomes tan(A+B) = -1.

5. How can I remember the tangent sum formula?

One way to remember the tangent sum formula is to think of it as "the sum of tangents over one minus the product of tangents". You can also use mnemonic devices like "SOHCAHTOA" (Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent) to help remember the trigonometric identities.

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