What is the trigonometric identity used to simplify this expression?

• cocopops12
In summary, a trigonometric identity is an equation that is true for all values of the variables involved and is used to simplify mathematical expressions involving trigonometric functions. They provide shortcuts for simplifying complex expressions and a commonly used example is the Pythagorean identity. Knowing which identity to use requires understanding of trigonometric functions and common mistakes to avoid include not properly distributing negative signs.
cocopops12

Could anyone please tell me how are those two expressions equivalent?! what are the identities used?

It's not a trig identity

$$\frac{1}{1-\sin z} = \frac{1+\sin z}{1+\sin z} \frac{1}{1-\sin z} = \frac{1+\sin z}{1-\sin^2 z}$$

1. What is a trigonometric identity?

A trigonometric identity is an equation that is true for all values of the variables involved. It is used to simplify mathematical expressions involving trigonometric functions, such as sine, cosine, and tangent.

2. How do trigonometric identities help simplify expressions?

Trigonometric identities provide shortcuts for simplifying complex expressions involving trigonometric functions. They allow us to replace one expression with another that is equivalent but simpler to work with.

3. Can you provide an example of a commonly used trigonometric identity?

One commonly used trigonometric identity is the Pythagorean identity, which states that sin^2(x) + cos^2(x) = 1. This identity is frequently used to simplify expressions involving sine and cosine functions.

4. How do I know when to use a specific trigonometric identity?

Knowing which trigonometric identity to use in a given situation comes with practice and experience. It is important to have a good understanding of the properties of trigonometric functions and how they relate to each other in order to determine which identity is most appropriate for simplifying a given expression.

5. Are there any common mistakes to avoid when using trigonometric identities?

One common mistake when using trigonometric identities is forgetting to properly distribute negative signs. It is important to pay attention to the signs of the terms in an expression when applying trigonometric identities, as a simple mistake can lead to an incorrect solution.

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