SOLUTION: when tanxsin^2x=tanx, and looking at the intervals [0,2pie) why is 0 and pie the only solutions for x? Shouldn't the solutions also include pie/2 and 3pie/2?

Algebra ->  Trigonometry-basics -> SOLUTION: when tanxsin^2x=tanx, and looking at the intervals [0,2pie) why is 0 and pie the only solutions for x? Shouldn't the solutions also include pie/2 and 3pie/2?      Log On


   

Question 503172: when tanxsin^2x=tanx, and looking at the intervals [0,2pie) why is 0 and pie the only solutions for x? Shouldn't the solutions also include pie/2 and 3pie/2?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since this means that




which is undefined (since you CANNOT divide by zero).


The same applies when


So because these values make the tangent function undefined, this means that they are NOT part of the domain. So this means that they are NOT part of the solution set (since everything in the solution set must be in the domain)