Question 860852
Find to the nearest degree the solution set of 2tanx=1+3cotx over the domain {0<=x<=360}
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{{{2tan(x)=1+3cot(x)}}}
{{{2tan(x)=1+(3/tan(x))}}}
{{{2tan(x)-(3/tan(x))=1}}}
LCD:tan(x)
{{{2tan^2(x)-3=tan(x)}}}
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.