SOLUTION: Solve the following equation, giving the exact solutions which lie in [0, 2π). (Enter your answers as a comma-separated list.) tan^2(x) = 3/2 sec^2x

Algebra ->  Trigonometry-basics -> SOLUTION: Solve the following equation, giving the exact solutions which lie in [0, 2π). (Enter your answers as a comma-separated list.) tan^2(x) = 3/2 sec^2x       Log On


   

Question 1078821: Solve the following equation, giving the exact solutions which lie in [0, 2π). (Enter your answers as a comma-separated list.)
tan^2(x) = 3/2 sec^2x

Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20066) About Me  (Show Source):
You can put this solution on YOUR website!
tan%5E2%28x%29+=+expr%283%2F2%29sec%5E2%28x%29

tan%5E2%28x%29+=+expr%283%2F2%29%281%2Btan%5E2%28x%29%5E%22%22%29

Multiply both sides by 2

2tan%5E2%28x%29+=+3%281%2Btan%5E2%28x%29%5E%22%22%29

2tan%5E2%28x%29+=+3%2B3tan%5E2%28x%29

-3+=+3tan%5E2%28x%29

-1+=+tan%5E2%28x%29

If you take square roots of both sides, what can you 
say about the solution(s)?

Edwin

Answer by ikleyn(52932) About Me  (Show Source):
You can put this solution on YOUR website!
.
Solve the following equation, giving the exact solutions which lie in [0, 2π). (Enter your answers as a comma-separated list.)
tan^2(x) = 3/2 sec^2x
~~~~~~~~~~~~~~~~~~~~ 

tan%5E2%28x%29 = %283%2F2%29%2Asec%5E2%28x%29   --->

sin%5E2%28x%29%2Fcos%5E2%28x%29 = %283%2F2%29%2A%281%2Fcos%5E2%28x%29%29   --->  (multiply both sides by cos^2(x). You will get)

sin%5E2%28x%29 = 3%2F2  --->

The solution DOES NOT exist since the left side is <= 1, while the right side is > 1.