Proving the Identity: sinA/(1+cosA)=tan(A/2)

  • Thread starter Thread starter brandon26
  • Start date Start date
  • Tags Tags
    Identity
Click For Summary
SUMMARY

The identity sinA / (1 + cosA) = tan(A/2) can be proven using the double angle formulas for sine and cosine. Specifically, the double angle formula for cosine, cos(2θ) = 1 - 2sin²(θ), simplifies the left-hand side of the equation. By substituting and manipulating the expressions, the identity holds true. This proof is essential for understanding trigonometric identities and their applications in calculus.

PREREQUISITES
  • Understanding of trigonometric identities
  • Familiarity with the double angle formulas for sine and cosine
  • Basic algebraic manipulation skills
  • Knowledge of tangent and its relationship to sine and cosine
NEXT STEPS
  • Study the derivation of the double angle formulas for sine and cosine
  • Practice proving other trigonometric identities
  • Explore the applications of trigonometric identities in calculus
  • Learn about the unit circle and its role in trigonometric functions
USEFUL FOR

Students studying trigonometry, mathematics educators, and anyone looking to deepen their understanding of trigonometric identities and their proofs.

brandon26
Messages
107
Reaction score
0
Prove the identity:

sinA / (1+cosA) = tan (A/2).

Im going no where with this, please help?:confused: :confused:
 
Physics news on Phys.org
use the double angle formula for cos2ø.
 
Sorry I don't understand. And I am trying to apply the double angle formulae but I am just getting confused.
 
Problem solved...No need to reply
 

Similar threads

How to prove this trigonometry equation?
  • · Replies 8 ·
Replies
8
Views
2K
Further Trigonometry Identity (Proving question)
  • · Replies 1 ·
Replies
1
Views
2K
Prove : (1+cosA - sinA)/(1+cosA + sinA) = secA - tanA
  • · Replies 9 ·
Replies
9
Views
12K
Proving: cosA/(1-tanA) + sinA/(1-cotA) = sinA + cosA
  • · Replies 6 ·
Replies
6
Views
2K
Particle dynamics (mechanics): inclined plane, pulley, two blocks
  • · Replies 14 ·
Replies
14
Views
3K
Proving tan2A = 2tanA/1-tan^2A: A Trig Identity Example
  • · Replies 1 ·
Replies
1
Views
4K
How to get from tan(a)/tan(b) to sin(a)/sin(b) or something simmilar
  • · Replies 25 ·
Replies
25
Views
3K
Solve Mcos^2(x) + Ncos(x) – 3 = 0 for M & N | Trig Help
  • · Replies 4 ·
Replies
4
Views
3K
Trying to prove a trig identity
  • · Replies 4 ·
Replies
4
Views
3K
Changing ##\tan\frac{x}{2}## to ##\cos x## for a proof
  • · Replies 8 ·
Replies
8
Views
2K