Trig Equations With Undefined Values

[Ellipses]

Homework Statement

1. Simplify:
[sin(x-pi) / cos(pi - x)] - [tan(x-3pi/2) / -tan(pi + x)

2. Solve:
1 - tan(2x + pi/2) = 0, 0 ≤ x ≤ 2pi

Homework Equations

cos(x - y) = cosxcosy + sinxsiny

sin(x - y) = sinxcosy + cosxsiny

tan(x + y) = tanx + tany / 1-tanxtany

tan (x - y) = tanx - tany / 1 +tanxtany

The Attempt at a Solution

For 1. I managed to expand everything according to the compound angle formulas listed above. Then I used the unit circle to come up with some values, which left me with:

[-cosx / -cosx] - [tanx-tan(3pi/2) / 1 + tanxtan(3pi/2)]
alskdjaslkdjalskdjalskdjalskdj -[(0 + tanx) / 1-(0)tanx]

The problem is that I don't know what to do with tan(3pi/2) because it's undefined...
The same problem persists for 2. I expanded but I don't know what to do with the undefined values. Please help!

Thank you in advance!

 

[LCKurtz]

Your problem is that the formula $$\tan(a-b)=\frac{\tan a -\tan b}{1 + \tan a \tan b}$$doesn't work for $a$ or $b$ is an odd multiple of $\pi/2$. Try writing$$
\tan(a-b) = \frac{\sin(a-b)}{\cos(a-b)}$$and use the addition formulas on that. That will work even when $\pi/2$ is involved.