# Help proving trigonometric identity

• blondie1125
In summary, proving a trigonometric identity involves using algebraic manipulation and well-known trigonometric identities, as well as properties of trigonometric functions. Some common tips include starting with the more complicated side, simplifying using algebra, and working with one side at a time. A calculator cannot be used to prove identities, and common mistakes include not simplifying enough and not following the order of operations. Alternative methods, such as geometric proofs and complex numbers, may be used but are not necessary for simpler identities.
blondie1125

## Homework Statement

cos$\theta$$/$1-tan$\theta$+sin$\theta$/1-cot$\theta$=sin$\theta$+cos$\theta$

## The Attempt at a Solution

blondie1125 said:

## Homework Statement

cos$\theta$$/$1-tan$\theta$+sin$\theta$/1-cot$\theta$=sin$\theta$+cos$\theta$
The rules of this forum say that you need to show an attempt. What have you tried?

Also, what you have written is very ambiguous. Is this the identity you are trying to prove?
$$\frac{cos(\theta)}{1 - tan(\theta)} + \frac{sin(\theta)}{1 - cot(\theta)} = sin(\theta) + cos(\theta)$$

It obviously just skipped Blondie's mind that maybe points 2 and 3 should be filled in also.

## 1. How do you prove a trigonometric identity?

To prove a trigonometric identity, you typically use algebraic manipulation and well-known trigonometric identities. You may also use the properties of the trigonometric functions, such as the Pythagorean identities or the double angle identities. It is important to work with one side of the equation at a time and manipulate it until it is equal to the other side.

## 2. What are some common tips for proving trigonometric identities?

Some common tips for proving trigonometric identities include starting with the more complicated side of the equation, simplifying both sides using algebraic manipulation, and using known trigonometric identities and properties. It is also helpful to remember to work with one side of the equation at a time and to make sure to show all steps and work clearly.

## 3. Can you use a calculator to prove trigonometric identities?

No, you cannot use a calculator to prove trigonometric identities. Proving an identity requires algebraic manipulation and the use of known trigonometric identities and properties. A calculator may be used to check your work, but it cannot be used as a tool for proving identities.

## 4. What are some common mistakes when proving trigonometric identities?

One common mistake when proving trigonometric identities is not simplifying both sides of the equation enough. It is important to use algebraic manipulation to simplify and transform each side until they are equal. Another mistake is not following the order of operations, which can lead to incorrect solutions. It is also important to be familiar with the properties and identities of trigonometric functions to avoid errors.

## 5. Are there any alternative methods for proving trigonometric identities?

Yes, there are alternative methods for proving trigonometric identities, such as using geometric proofs or using complex numbers. However, these methods may be more advanced and may not be necessary for simpler identities. It is important to be familiar with the basic algebraic and trigonometric methods before attempting alternative methods.

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