# Trig proof, I am getting a neg instead of pos.

• jrjack
I guess I just needed to see it written out. Thank you for your help.In summary, to prove that the left side of the equation [cscx/(1+cscx)] - [cscx/(1-cscx)] equals the right side of 2 sec^2 x, the steps are:1. Get a common denominator and subtract.2. Distribute cscx in the numerator and multiply out the denominator.3. Combine like terms in the numerator and use the identity in the denominator.4. Use the reciprocal of cot=1/tan and divide the numerator by the denominator.5. Change csc and tan to sin and cos.6. Cross cancel and multiply to get -2sec^
jrjack

## Homework Statement

[cscx/(1+cscx)] - [cscx/(1-cscx)] = 2 sec^2 x

## Homework Equations

prove the left side equals the right side

## The Attempt at a Solution

1. get common denominator and subtract, [cscx(1-cscx)-cscx(1+cscx)]/[(1+cscx)(1-cscx)]

2. distribute cscx in numerator [cscx-csc^2 x-cscx-csc^2 x]/
and multiply out denominator [1-csc^2 x]

3. combine like terms numerator [-2csc^2x]/
identity in denominator (cot^2 x)

4. reciprocal of cot=1/tan, then divide num/dem (-2csc^2 x)(tan^2 x)

5. change csc and tan to sin, cos [-2(1/sin^2 x)] [(sin^2 x)/(cos^2x)]

6. cross cancel and multiply -2(1/cos^2 x) or -2sec^2 x

I have checked this several times and cannot figure out why I get -2 instead of 2.

1-csc(x)^2=(-cot(x)^2), isn't it?

Thats it. Thanks.

I knew I was overlooking something simple.

## 1. Why am I getting a negative value instead of a positive value in my trigonometry proof?

This is most likely due to an error in your calculations. Check your work carefully and make sure you are using the correct signs and following the correct steps in your proof.

## 2. How can I check if my trigonometry proof is correct?

You can check your proof by plugging in the values from your problem into your equations and seeing if they result in the same value on both sides of the equation. You can also ask a teacher or peer to review your work.

## 3. What are some common mistakes that lead to getting a negative value in a trigonometry proof?

Some common mistakes include using the wrong trigonometric identities or formulas, mixing up the order of operations, and forgetting to distribute negative signs. It is important to double check your work and understand the steps in your proof.

## 4. Can a negative value be correct in a trigonometry proof?

Yes, a negative value can be correct in a trigonometry proof. It is important to pay attention to the context of the problem and understand if a negative value makes sense in the given scenario.

## 5. How can I avoid getting a negative value in my trigonometry proof?

To avoid getting a negative value, it is important to carefully follow the steps in your proof and check your work for errors. It can also be helpful to practice using trigonometric identities and formulas to become more familiar with them.

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