- #1
ciubba
- 65
- 2
Prove the following identity: [tex]\frac{1-tan^2(\theta)}{1-cot^2(\theta)}=1-sec^2(\theta)[/tex]
By tan/sec identity,
[tex]\frac {2-sec^2(\theta)}{2-csc^2(\theta)}[/tex]
separated the variables
[tex]\frac {2}{2-csc^2}- \frac {sec^2}{2-csc^2}[/tex]
There's absolutely nothing useful I can do with either of those terms, so that approach is useless. I also tried putting everything into terms of sin and cos and simplifying to get
[tex]\frac {sin^2- \frac {2sin^2}{cos^2}}{2sin^2-1}[/tex]
but that wasn't helpful either. I'm assuming that I need to simplify to -tan^2, but I can't find any way to do that.
By tan/sec identity,
[tex]\frac {2-sec^2(\theta)}{2-csc^2(\theta)}[/tex]
separated the variables
[tex]\frac {2}{2-csc^2}- \frac {sec^2}{2-csc^2}[/tex]
There's absolutely nothing useful I can do with either of those terms, so that approach is useless. I also tried putting everything into terms of sin and cos and simplifying to get
[tex]\frac {sin^2- \frac {2sin^2}{cos^2}}{2sin^2-1}[/tex]
but that wasn't helpful either. I'm assuming that I need to simplify to -tan^2, but I can't find any way to do that.