Cos Trig Identity: Deriving Formula for Circuits Analysis

  • Context: MHB 
  • Thread starter Thread starter paulmdrdo1
  • Start date Start date
  • Tags Tags
    Cos Identity Trig
Click For Summary
SUMMARY

The discussion focuses on deriving the trigonometric identity for the expression $$\cos(A+B)\cos(A+C)$$, which is essential for circuits analysis. The established identity is $$\cos(A+B) \, \cos(A+C) = \frac12 \left[ \cos(2A + B + C) + \cos(B-C) \right]$$. This formula is crucial for simplifying calculations in electrical engineering contexts, particularly in analyzing circuit behaviors involving phase angles.

PREREQUISITES
  • Understanding of trigonometric identities
  • Familiarity with circuit analysis concepts
  • Basic knowledge of phase angles in electrical engineering
  • Proficiency in mathematical derivations
NEXT STEPS
  • Study the derivation of trigonometric identities in detail
  • Explore applications of trigonometric identities in circuit analysis
  • Learn about phase shift calculations in AC circuits
  • Investigate the use of complex numbers in circuit analysis
USEFUL FOR

Electrical engineering students, circuit designers, and anyone involved in analyzing AC circuits will benefit from this discussion, particularly those looking to deepen their understanding of trigonometric applications in engineering contexts.

paulmdrdo1
Messages
382
Reaction score
0
Hello. Do you guys know if there is an identity related to this expression

$$\cos(A+B)\cos(A+C)$$

If so, can you help me how to derive it? I need it for the derivation of the formula from my circuits analysis course. Thanks.
 
Mathematics news on Phys.org
Apparently, you can change it from a product to a sum like this:
$$\cos(A+B) \, \cos(A+C) = \frac12 \left[ \cos(2A + B + C) + \cos(B-C) \right].$$
Does that help?
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 3 ·
Replies
3
Views
3K
Replies
9
Views
3K
Replies
4
Views
2K
Replies
54
Views
4K
  • · Replies 4 ·
Replies
4
Views
4K
  • · Replies 32 ·
2
Replies
32
Views
3K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 3 ·
Replies
3
Views
3K