SOLUTION: Find to the nearest degree the solution set of 2tanx=1+3cotx over the domain {0<=x<=360}

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Question 860852: Find to the nearest degree the solution set of 2tanx=1+3cotx over the domain {0<=x<=360}
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find to the nearest degree the solution set of 2tanx=1+3cotx over the domain {0<=x<=360}
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2tan%28x%29=1%2B3cot%28x%29
2tan%28x%29=1%2B%283%2Ftan%28x%29%29
2tan%28x%29-%283%2Ftan%28x%29%29=1
LCD:tan(x)
2tan%5E2%28x%29-3=tan%28x%29
2tan^2x-tanx-3=0
(2tanx-3)(tanx+1)=0
..
2tanx-3=0
tanx=3/2
x=56.3, 236.3 deg (in quadrants I and III in which tan>0)
or
tanx+1=0
tanx=-1
x=135, 315 deg (in quadrants II and IV in which tan<0)
Let me know if my solution is correct, helpful and understandable.