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**benny92000** If **tan 4(x) = 2cot4(x)** , and 0<x<180 (< equals less than or equal to), then x=?

The answer is 13.7, 76.3, 103.7, 166.3 (degrees).

I graphed the two equations. I graphed tan4x and 2/(tan4x) In the graphs, all of these degree measures do show points of intersection. However, I also see other points of intersection between 0 to 180 that are not in the answer set. Is there an explanation for this?

Additionally, my book said to solve for x by first making it 2/(tan4x) = tan4x Once you solve for x this way, the answer is 13.7. Then they say that since it is between 0-180, we get our 4 angle measures from the answer.

I am confused about this part. I understand that 13.7 and 166.3 will be solutions in the first and second quadrants, but why will 76.3 and 103.7 be solutions?

I hope that made sense. Thanks.