MHB Cos Trig Identity: Deriving Formula for Circuits Analysis

Click For Summary
The discussion focuses on deriving a cosine trigonometric identity for the expression cos(A+B)cos(A+C) relevant to circuit analysis. It is noted that this expression can be transformed into a sum using the identity cos(A+B)cos(A+C) = 1/2 [cos(2A + B + C) + cos(B-C)]. This transformation is crucial for simplifying calculations in circuit analysis. Participants seek clarification on the derivation process and its applications. Understanding this identity can enhance problem-solving in electrical 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?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

Undergrad Adding trig functions with different amplitudes
  • · Replies 5 ·
Replies
5
Views
2K
MHB Finding the domain of this function.
  • · Replies 5 ·
Replies
5
Views
2K
MHB Solving trig equation cos(x)=sin(x) + 1/√3
  • · Replies 3 ·
Replies
3
Views
3K
MHB Trig Identity Problem: Solve cos2(x) + sin(x) = sin2(x) for 0^0<=x<=180^0
  • · Replies 9 ·
Replies
9
Views
3K
Using Euler's formula to prove trig identities using "sum to product" technique
  • · Replies 4 ·
Replies
4
Views
2K
Proving trig identities -- Is the method related to the unit circle?
  • · Replies 54 ·
2
Replies
54
Views
4K
Trig identities and complex numbers help.
  • · Replies 4 ·
Replies
4
Views
3K
I badly with general answers to trig equations. (Using identities)
  • · Replies 32 ·
2
Replies
32
Views
3K
MHB Establishing Identities - Possible Misprint on Worksheet
  • · Replies 9 ·
Replies
9
Views
2K
Learning Trig Identities: Deriving the Essentials
  • · Replies 3 ·
Replies
3
Views
3K