Changing back after substitution

[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.

 

[haruspex]

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