Is 2tan2b the Simplified Form of tan(45° + b) - tan(45° - b)?

  • Thread starter philipp2020
  • Start date
In summary, The conversation is about simplifying the expression tan (45° + b) - tan (45° -b). The person asking the question has used the Theorems for Addition on both sides, but is not sure if their result is correct. Another person suggests double checking the tangent sum and difference identities and mentions that the numerator should only be 4 tan b, leading to a final simplified expression of 2 * tan 2b.
  • #1
philipp2020
34
0
hi

i have a question on a simplification

tan (45° + b) - tan (45° -b)

Then I put on both sides the Theorems for Addition. But I am not sure if my result is right. What is most possible simplification here?

is it 1 + 4 tan b / 1 - tan^2 b ?

Thanks very much for an answer.

Greetings

Philipp
 
Last edited:
Physics news on Phys.org
  • #2
Double check the tangent sum and difference identities. Your denominator is good, but I can't figure out what mistake you could have made to get the numerator that you did.

If you get the numerator correct, there's another identity that allows you to simplify the fraction.
 
  • #3
ah so the numerator is only 4 tan b and not plus 1 yes...

oh ok... i see

then at the end it will be just 2 * tan 2b
 

FAQ: Is 2tan2b the Simplified Form of tan(45° + b) - tan(45° - b)?

What is tangens and why is it important in simplification?

Tangens is a mathematical function that relates the ratio of the opposite side of a right triangle to the adjacent side. It is important in simplification because it allows us to easily convert between angles and sides of a triangle and simplify complex expressions involving trigonometric functions.

How is tangens simplified?

Tangens can be simplified using trigonometric identities and basic algebraic manipulations. For example, the identity tan(x) = sin(x)/cos(x) can be used to simplify expressions involving tangens. Additionally, the use of common trigonometric values and special triangles can also help simplify tangens expressions.

Can tangens ever be undefined?

Yes, tangens can be undefined for certain values of the angle x. This occurs when the cosine of x is equal to 0, since division by 0 is undefined. In these cases, the tangent function is considered to be undefined or "does not exist".

Is there a limit to how much tangens can be simplified?

No, there is no limit to how much tangens can be simplified. As long as the expression follows the rules of algebra and trigonometry, it can be simplified further. However, in some cases, the simplified form may be considered "good enough" and further simplification may not be necessary.

How can simplification on tangens be applied in real life?

Simplification on tangens can be applied in various fields such as engineering, physics, and navigation. For example, it can be used to calculate the height of a building or the distance between two points using trigonometric functions and simplified tangens expressions. It can also help in solving real-life problems involving angles and distances, such as finding the angle of elevation or depression in surveying or construction projects.

Similar threads

To prove a trigonometric identity with tan() and cot()
Replies
2
Views
1K
Half Angle Formula for Tangent
Replies
15
Views
3K
Converting standard to polar form
Replies
6
Views
2K
Trig, find tan A and tan B (no numbers given)
Replies
5
Views
2K
Solving equations of the form ##a\sin\theta+b\cos\theta = c##
Replies
2
Views
2K
Trigonometric equation solving 2cos x=tan x
Replies
6
Views
2K
Computing arctan (inverse tan) function
Replies
10
Views
3K
Solving a Trigonometry Problem with Tan A and Tan B
Replies
2
Views
2K
Trig Identities: Simplifying Expressions with Cotangent, Secant, and Cosecant
Replies
17
Views
2K
Calculate the Unknown Angle of a Right Triangle
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top