Question 334139
Find all values of t in the interval [0,2π] if {{{cot(t)-3*tan(t)=0}}}
<pre><font size = 3 color = "indigo"><b>
{{{Cot(t)-3*Tan(t)=0}}}

Use the identity {{{Tan(theta)=1/Cot(theta)}}}

{{{Cot(t)-3*(1/Cot(t))=0}}}

Multiply through by {{{Cot(t)}}}

{{{Cot^2(t)-3=0}}}

{{{Cot^2t=3}}}

Use the principle of square roots:

{{{Cot(t)="" +- sqrt(3)}}}

The solutions are all angles with a reference angle of {{{pi/6}}}

{{{pi/6}}}, {{{5pi/6}}}, {{{7pi/6}}}, {{{11pi/6}}}

Edwin</pre>