Explaining steps in simplification

[exequor]

can someone explain to me the stages that are missing in the expression in the attached picture. i think that it has to do with identities but in the book that i got it from did not explain clearly how they went from one line to another. i will appreciate the help very much. all i am trying to do is to understand how to go from one line to the other.

 

[arildno]

No wonder you're stuck; the lines contain a mistake. (Setting "theta"=15 in the last line yields 1.1=sin30)
The transformation of the righthand sides in line 2 to 3 is the sine summation formula

 

[tacman]

Sure, I would be happy to explain the steps in simplification. The process of simplification involves transforming a complex expression into a simpler form by applying various mathematical rules and properties. This can be done in several stages, including:

1. Simplifying within parentheses: If the expression contains parentheses, start by simplifying the terms within them using the appropriate rules, such as the distributive property or combining like terms.

2. Simplifying exponents: Next, simplify any exponents in the expression by applying the laws of exponents, such as the power rule or the product rule.

3. Combining like terms: Look for terms that are similar and combine them using the commutative and associative properties. This will reduce the number of terms in the expression.

4. Applying identities: Use identities, such as the Pythagorean identity or the double angle identity, to simplify the expression further.

5. Factoring: If the expression can be factored, do so to simplify it. This involves breaking down the expression into smaller parts that can be simplified individually.

6. Canceling out terms: If there are any terms that are the same on the top and bottom of a fraction, they can be canceled out to simplify the expression.

7. Simplifying fractions: If the expression contains fractions, simplify them by finding the lowest common denominator and reducing the fractions to their simplest form.

It is important to note that the order in which these steps are applied may vary depending on the expression. Additionally, some expressions may require multiple iterations of these steps to fully simplify them. I hope this helps in understanding the process of simplification.