Need help with a problem (sum of two angles)

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In summary, to solve for the exact value of tan(15°) using the difference formula, combine the fractions in the numerator and denominator, simplify the complex fraction, and rationalize the denominator. This will result in the solution of 2 - √3.
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Charlie Prieto
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Homework Statement



Hello, all. This here's the problem: Use the difference formula to solve for the exact value of tan(15°).

Homework Equations

The Attempt at a Solution


I've solved it up until this point:
I used the formula to get (tan(45°)-tan(30°)) / (1 + tan(45°)tan(30°)).
(1 - (sqrt(3)/3)) / (1 + (1)(sqrt(3)/3)). How do I get 2 - sqrt(3), which I know is the answer, from the point I'm at?.
 
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  • #2
Charlie Prieto said:

Homework Statement



Hello, all. This here's the problem: Use the difference formula to solve for the exact value of tan(15°).

Homework Equations

The Attempt at a Solution


I've solved it up until this point:
I used the formula to get (tan(45°)-tan(30°)) / (1 + tan(45°)tan(30°)).
(1 - (sqrt(3)/3)) / (1 + (1)(sqrt(3)/3)). How do I get 2 - sqrt(3), which I know is the answer, from the point I'm at?.
In the numerator, combine the fractions 1/1 and -√3/3. Do the same in the denominator, which is only slightly different. At this point, you'll have what is called a complex fraction, one in which both the numerator and denominator are themselves fractions.

To simplify a complex fraction that looks like this...
$$\frac{ \frac{a + b}{c} }{\frac{ e + f}{c}}$$
multiply by 1 in the form of c/c.

Finally, you'll need to rationalize the denominator,
 

Related to Need help with a problem (sum of two angles)

What is the sum of two angles?

The sum of two angles is the total measure of both angles combined. This can be found by adding the measure of the two angles together.

How do I find the sum of two angles?

To find the sum of two angles, simply add the measure of the two angles together. For example, if one angle is 45 degrees and the other is 60 degrees, the sum would be 105 degrees.

Can two angles with different measurements have the same sum?

Yes, two angles with different measurements can have the same sum. For example, an angle measuring 30 degrees and an angle measuring 60 degrees both have a sum of 90 degrees.

What is the maximum sum of two angles?

The maximum sum of two angles is 180 degrees. This is because the maximum measure of an angle is 180 degrees, and adding two angles together cannot exceed this maximum measure.

Can the sum of two angles be negative?

No, the sum of two angles cannot be negative. Angles are always measured in degrees or radians, which are positive values. Therefore, the sum of two angles will always be a positive value.

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