What is the fundamental identity used to prove csc2α - 1 = cos2α / csc2α?

Click For Summary
SUMMARY

The discussion focuses on proving the trigonometric identity csc²α - 1 = cos²α / csc²α using Pythagorean identities. The initial step involves dividing the numerator by the denominator on the left side of the equation. The identity csc(α) = 1/sin(α) is also highlighted as a crucial component in the proof process. Participants emphasize the importance of understanding these foundational identities to successfully complete the proof.

PREREQUISITES
  • Understanding of trigonometric identities, specifically Pythagorean identities.
  • Familiarity with cosecant and cosine functions.
  • Basic algebraic manipulation skills.
  • Knowledge of the relationship between sine and cosecant functions.
NEXT STEPS
  • Study Pythagorean identities in trigonometry.
  • Learn how to manipulate trigonometric functions algebraically.
  • Explore the derivation and applications of cosecant functions.
  • Practice proving various trigonometric identities.
USEFUL FOR

Students studying trigonometry, educators teaching trigonometric identities, and anyone looking to strengthen their understanding of algebraic manipulation in trigonometric proofs.

SkiingAlta
Messages
19
Reaction score
0

Homework Statement


Okay, so this is some trig I learned last year but have since forgotten. If you can give me the first step, I can solve the rest on my own. The given statement is true and you have to prove why using Pythagorean Identities.

csc2\alpha-1 = cos2\alpha
________
csc2\alpha
 
Physics news on Phys.org
The first step is to just divide the numerator on the left side by the denominator. Try it and you will see how it makes sense.
 
You are a little wrong there. I don't have to prove it. YOU have to prove it. csc(alpha)=1/sin(alpha). Just try it. Ok?
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 69 ·
3
Replies
69
Views
9K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 10 ·
Replies
10
Views
2K
Replies
4
Views
2K
Replies
34
Views
4K
  • · Replies 5 ·
Replies
5
Views
2K
Replies
6
Views
2K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 13 ·
Replies
13
Views
3K