Solve Lie Algebra Easily: No Math Theory Needed

[Silviu]

Hello! Is there any rule to do sums and products like the one in the attached picture (Lie.png) without going through all the math theory behind? I understand the first (product) and last (sum) terms, but I am not sure I understand how you go from one to another.
Thank you!

 

[jvicens]

Hello there,

Thank you for your question. The rule that you are referring to is known as the "product-to-sum" rule in mathematics. It is a way of simplifying and rewriting expressions that involve products and sums. This rule is based on the trigonometric identity: sin(x)cos(y) = 1/2(sin(x+y) + sin(x-y)).

To use this rule, you need to first identify the terms that involve products and sums in your expression. In the attached picture, the first term involves a product of two trigonometric functions (sin(3x)cos(2x)), while the last term involves a sum of two trigonometric functions (sin(3x+2x)).

To go from the product to the sum, you can use the identity mentioned above. In this case, you can rewrite the first term as 1/2(sin(3x+2x) + sin(3x-2x)). This is the same as the last term in the expression.

It is important to note that this rule only works for specific types of expressions involving products and sums of trigonometric functions. It may not work for other types of expressions.

I hope this helps to clarify the rule for you. If you have any further questions, please let me know.