Stuck on a trigonometric identity proof....

Click For Summary
SUMMARY

The trigonometric identity proof discussed is $\frac{1 - \cos A}{1 + \cos A} = (\cot A - \csc A)^2$. The solution involves converting cotangent and cosecant into sine and cosine, followed by algebraic manipulation. A key step includes multiplying the left side by $\frac{1 - \cos A}{1 - \cos A}$, leading to the expression $\frac{1 - 2\cos A + \cos^2 A}{\sin^2 A}$. This approach successfully demonstrates the equivalence of both sides of the identity.

PREREQUISITES
  • Understanding of trigonometric identities
  • Familiarity with sine and cosine functions
  • Knowledge of cotangent and cosecant functions
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the derivation of trigonometric identities
  • Learn about the Pythagorean identities in trigonometry
  • Explore advanced algebraic techniques for simplifying trigonometric expressions
  • Practice proving other trigonometric identities using similar methods
USEFUL FOR

Students studying trigonometry, mathematics educators, and anyone looking to enhance their skills in proving trigonometric identities.

Riwaj
Messages
12
Reaction score
0
$\frac{1 -\cos A}{1 + \cos A} = (\cot A - \csc A)^2$
 
Last edited by a moderator:
Mathematics news on Phys.org
Re: please prove it i am stuck ...

Riwaj said:
$\frac{1 -\cos A}{1 + \cos A} = (\cot A - \csc A)^2$
Hi Riwaj,

What did yo try so far ?
 
Re: please prove it i am stuck ...

My approach would be to change the cosecant and cotangent on the right side to sine and cosine, then do the indicated operations on the right.
 
Here's the start of another approach:

$$\frac{1 - \cos x}{1 + \cos x} \cdot \frac{1 - \cos x}{1 - \cos x} = \frac{1 - 2\cos x + \cos^2 x}{\sin^2 x}$$
 
oh ... thank you everyone i got it now
 

Similar threads

High School Trigonometric Identity involving sin()+cos()
  • · Replies 11 ·
Replies
11
Views
2K
High School Can 2(sinx) be called a 'trigonometric function'?
  • · Replies 28 ·
Replies
28
Views
3K
MHB Solve Situational Problems Involving Trigonometric Identities
  • · Replies 3 ·
Replies
3
Views
2K
MHB How to Prove a Trigonometric Identity Involving x, y, and z?
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Is this a Trigonometric Identity?
  • · Replies 20 ·
Replies
20
Views
2K
MHB Can you prove the following two difficult trigonometric identities?
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Question ,trigonometric identities equation and functions ?
  • · Replies 4 ·
Replies
4
Views
2K
MHB What is the Proof for the Trigonometric Sum Identity?
  • · Replies 2 ·
Replies
2
Views
1K
High School What values of m as a function of q satisfy this trigonometric equation?
  • · Replies 5 ·
Replies
5
Views
1K
MHB Simple Trigonometric Identities
  • · Replies 9 ·
Replies
9
Views
3K