A problem in Trigonometry (Properties of Triangles)

In summary, the problem at hand is to prove that in any triangle ABC, the expression (b+c-a) (cot B/2 + cot C/2) is equal to 2a cot A/2. The respondent tried multiple approaches to solve the problem, such as using the sine rule and the sum of angles in a triangle being 180 degrees, but was unsuccessful in finding a solution.
  • #1
Wrichik Basu
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In any triangle ABC, prove that $$(b+c-a) \left( \cot {\frac {B}{2}} + \cot {\frac {C}{2}} \right)=2a \cot {\frac {A}{2}} $$
 
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  • #2
Wrichik Basu said:
In any triangle ABC, prove that $$(b+c-a) \left( \cot {\frac {B}{2}} + \cot {\frac {C}{2}} \right)=2a \cot {\frac {A}{2}} $$

Did you try to solve this ?
Also you should not vandalise the template.
 
  • #3
Buffu said:
Did you try to solve this ?
Also you should not vandalise the template.

I tried in several ways, trying to change a, b, c to 2R sin A and like that, or trying the formulae for cot A/2, but got nowhere.
 
  • #4
Wrichik Basu said:
I tried in several ways, trying to change a, b, c to 2R sin A and like that, or trying the formulae for cot A/2, but got nowhere.
Use sine rule and A + B + C = 180.
 

1. What are the three basic trigonometric functions?

The three basic trigonometric functions are sine, cosine, and tangent. These functions relate the angles of a right triangle to the lengths of its sides.

2. How do you find the missing side length of a right triangle using trigonometry?

To find the missing side length of a right triangle using trigonometry, you can use the Pythagorean theorem (a² + b² = c²) or one of the trigonometric ratios (sin, cos, or tan) depending on the information given. If you have the length of one side and the measure of one angle, you can use sine or cosine. If you have the lengths of two sides, you can use tangent.

3. What are the primary properties of triangles that are used in trigonometry?

The primary properties of triangles that are used in trigonometry are the Pythagorean theorem, the sum of angles in a triangle (which is always 180 degrees), and the trigonometric ratios (sine, cosine, and tangent).

4. How do you use the Law of Sines and the Law of Cosines to solve problems in trigonometry?

The Law of Sines and the Law of Cosines are used to solve problems involving triangles that are not right triangles. The Law of Sines relates the lengths of the sides of a triangle to the sine of their opposite angles, while the Law of Cosines relates the lengths of the sides to the cosine of one of the angles. These laws can be used to find missing side lengths or angle measures in oblique triangles.

5. Can trigonometry be used in real-life applications?

Yes, trigonometry is used in many real-life applications, such as engineering, architecture, physics, and astronomy. It can be used to calculate distances, angles, and heights in various structures and objects. For example, trigonometry is used to design buildings and bridges, navigate ships, and predict the movement of planets and stars.

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