# Changing back after substitution

• silenzer
In summary, the conversation discusses using substitution and variable changes to simplify integration problems involving trigonometric and hyperbolic functions. The person has already attempted some problems but is still struggling and asks for help with one specific problem. They mention using double angle rules and dividing by cos^2(z)+sin^2(z) in their attempts.
silenzer

## Homework Statement

I've done 1-3 and 10-20, but these give me an extreme headache. Assume I know everything there is to know about integration and the trigonometric and hyperbolic functions.

Change the following into variables with x with...

4. (1/4) * sin(z) - (1/12) * sin^3(z) after having substituted with x+1 = 2tan(z);

5. -coth(z) after having substituted with x+1 = sinh(z);

6. (3/16) * sinh(2z)+(1/8)z after having substituted with x = cosh(z);

7. z - coth(z) after having substituted with x = sinh(z);

8. -(4/3) * cos^3(z) after having substituted with x+1 = 2sin(z);

9. tan(z) after having substituted with x - 1 = sin(z).

2.

## Homework Equations

Everything about integration and the hyperbolic and trigonometric functions.

## The Attempt at a Solution

I experimented with the double angle rules, dividing by cos^2(z)+sin^2(z), and pretty much everything else. If you could just show me the answer to one of those, it'd be greatly appreciated.

Can you write sin(z) in terms of tan(z)?

## 1. Can the original substance be recovered after substitution?

Yes, it is possible to change back to the original substance after substitution by reversing the process through a chemical reaction or physical separation.

## 2. Will the properties of the original substance be the same after changing back?

In most cases, the properties of the original substance will be restored after changing back. However, there may be slight variations depending on the nature of the substitution and the efficiency of the reversal process.

## 3. How is changing back after substitution different from a chemical reaction?

Changing back after substitution involves reversing the process of substitution, while a chemical reaction involves the formation of new substances through the rearrangement of atoms. Chemical reactions are usually irreversible, whereas changing back after substitution is potentially reversible.

## 4. What factors can affect the success of changing back after substitution?

The success of changing back after substitution depends on various factors such as the type of substitution, the efficiency of the reversal process, and external conditions like temperature, pressure, and presence of other substances.

## 5. Can changing back after substitution be used to purify substances?

Yes, changing back after substitution can be used as a purification method for certain substances. By selectively substituting impurities and then changing back to the original substance, the impurities can be removed, resulting in a purer product.

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