Double-Angle Formula: Solving for (1+\cosh(v))(\cosh(v)-\cos(u))

Ted123 · 2011-11-30T18:53:28+00:00

I need to get from \cosh^2(v)-2\cos(u)\cosh(v) + 4\cos^2(\frac{u}{2})\sinh^2(\frac{v}{2}) + 1 to (1+\cosh(v))(\cosh(v)-\cos(u)) using double angle formulae.

Thread starter Ted123
Start date Nov 30, 2011
Tags

Formula

In summary, the double-angle formula can be used to solve expressions involving trigonometric functions by substituting the variables with their half-angle equivalents and simplifying the equation. However, it is only applicable for angles between 0 and 90 degrees and may not work for certain values. In real-world applications, the formula can be helpful in solving problems in fields such as physics, engineering, and geometry.

Nov 30, 2011

Ted123

I need to get from [tex]\cosh^2(v)-2\cos(u)\cosh(v) + 4\cos^2(\frac{u}{2})\sinh^2(\frac{v}{2}) + 1[/tex] to [tex](1+\cosh(v))(\cosh(v)-\cos(u))[/tex] using double angle formulae.

Physics news on Phys.org

Nov 30, 2011

susskind_leon

Turn the double angle formulae into half-angle formulae, then it should be a piece of cake.

1. What is the double-angle formula for solving (1+cos(v))(cos(v)-cos(u))?

The double-angle formula for solving (1+cos(v))(cos(v)-cos(u)) is (1+cos(v))(cos(v)-cos(u)) = 2cos(v/2)^2-2cos(u/2)^2.

2. How do you use the double-angle formula to solve for (1+cos(v))(cos(v)-cos(u))?

To use the double-angle formula, you can substitute cos(v) and cos(u) with their respective half-angle equivalents and then simplify the equation.

3. Can the double-angle formula be used to solve for other trigonometric expressions?

Yes, the double-angle formula can be used to solve for other trigonometric expressions such as (1+sin(v))(sin(v)-sin(u)), (1+tan(v))(tan(v)-tan(u)), and (1+cot(v))(cot(v)-cot(u)).

4. Are there any special cases or restrictions when using the double-angle formula?

Yes, the double-angle formula is only applicable when dealing with angles between 0 and 90 degrees. Additionally, the formula may not work for certain values of u and v, so it is important to check for any restrictions before using it.

5. How can the double-angle formula be useful in real-world applications?

The double-angle formula can be useful in real-world applications such as physics, engineering, and geometry where trigonometric functions are used to model and solve problems. It allows for simplification of complex expressions and can help in finding solutions to various equations.