Proving Trigonometric Identity: Double Angle Formula

In summary, the double angle formulas in trigonometry are equations that express the trigonometric functions of double the angle in terms of the trigonometric functions of the original angle. To prove these formulas, one can use trigonometric identities such as the Pythagorean identity and the sum and difference identities. Some common double angle identities include the sine, cosine, and tangent double angle identities. These formulas are important for simplifying expressions and solving equations, as well as finding exact values in scientific and engineering applications. One way to remember these formulas is by using the acronym "SOHCAHTOA" and doubling the angle in each equation while using the Pythagorean identity.
Physics news on Phys.org
  • #2
Use
[tex]\sin a \cos b = (\sin (a+b) + \sin(a-b))/2[/itex]
 
  • #3
Thanks! I will give that a go
 
  • #4
AlephZero said:
Use
[tex]\sin a \cos b = (\sin (a+b) + \sin(a-b))/2[/itex]

Thanks, I managed to do it using

[tex]
\cos a \sin b = (\sin (a+b) - \sin(a-b))/2
[/tex]

PROBLEM SOLVED!
 

1. What are the double angle formulas in trigonometry?

The double angle formulas in trigonometry are equations that express the trigonometric functions of double the angle in terms of the trigonometric functions of the original angle. These formulas are used to simplify trigonometric expressions and solve trigonometric equations.

2. How do you prove a double angle formula?

To prove a double angle formula, you typically start with the left side of the equation and use trigonometric identities, such as the Pythagorean identity and the sum and difference identities, to manipulate the expression until it is equivalent to the right side of the equation.

3. What are some common double angle identities?

Some common double angle identities include:

  • Sine double angle identity: sin(2x) = 2sin(x)cos(x)
  • Cosine double angle identity: cos(2x) = cos^2(x) - sin^2(x)
  • Tangent double angle identity: tan(2x) = 2tan(x) / (1 - tan^2(x))

4. Why are double angle formulas important?

Double angle formulas are important because they allow us to simplify trigonometric expressions and solve trigonometric equations. They also help us to find exact values of trigonometric functions, which is useful in many scientific and engineering applications.

5. How can I remember the double angle formulas?

One way to remember the double angle formulas is to use the acronym "SOHCAHTOA", which stands for "Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent". By remembering this phrase, you can easily derive the double angle formulas by doubling the angle in each of these equations and using the Pythagorean identity to simplify the expressions.

Similar threads

  • Calculus and Beyond Homework Help
Replies
5
Views
1K
  • Precalculus Mathematics Homework Help
Replies
6
Views
1K
Replies
4
Views
924
  • Precalculus Mathematics Homework Help
Replies
17
Views
1K
  • Introductory Physics Homework Help
Replies
8
Views
1K
Replies
18
Views
1K
  • Precalculus Mathematics Homework Help
Replies
1
Views
1K
  • Calculus and Beyond Homework Help
Replies
9
Views
859
  • General Math
Replies
1
Views
1K
  • General Math
Replies
20
Views
2K
Back
Top