SOLUTION: Hi, this problem is giving me a hard time. The problem is rad3*sin2x=cos2x. I'm supposed to find all solutions of this equation and these double angles are making me frustrated.

Algebra ->  Trigonometry-basics -> SOLUTION: Hi, this problem is giving me a hard time. The problem is rad3*sin2x=cos2x. I'm supposed to find all solutions of this equation and these double angles are making me frustrated.       Log On


   

Question 138440This question is from textbook Algebra and Trigonometry
: Hi, this problem is giving me a hard time. The problem is rad3*sin2x=cos2x. I'm supposed to find all solutions of this equation and these double angles are making me frustrated. Thank you for helping me out. This question is from textbook Algebra and Trigonometry

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
I suspect you are frustrated because you are trying to make this too difficult. If you are using the double angle formulas you are barking up the wrong tree.

Remember that sin%28alpha%29%2Fcos%28alpha%29=tan%28alpha%29

Let alpha=2x

Then sqrt%283%29%2Asin%282x%29=cos%282x%29 => sqrt%283%29%2Asin%28alpha%29=cos%28alpha%29

Now with a bit of algebra we can write: sin%28alpha%29%2Fcos%28alpha%29=1%2Fsqrt%283%29 which is to say tan%28alpha%29=1%2Fsqrt%283%29 => alpha=arctan%281%2Fsqrt%283%29%29 => alpha=pi%2F6

But alpha=2x , so 2x=pi%2F6 => x=pi%2F12. The periodicity of tan%28x%29 is pi, so the complete solution is x=pi%2F12%2Bk%2Api where k is any integer.