Question 1057643
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solve exactly over 0 ° &#8804; &#952; < 360° : 4cos^2&#952; - 4sin&#952; =5 
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<pre>
{{{4cos^2(theta) - 4*sin(theta)}}} = 5.

Replace {{{cos^2(theta)}}} by {{{1-sin^2(theta)}}} to make the equation uniform for {{{sin(theta)}}}. You will get

{{{4*(1-sin^2(theta)) - 4*sin(theta)}}} = 5,   or

{{{4*sin^2(theta) + 4*sin(theta) + 1}}} = 0,   or

{{{(2*sin(theta) + 1)^2}}} = 0.


Then

{{{2*sin(theta) + 1}}} = 0  --->  {{{sin(theta)}}} = {{{-1/2}}}  --->  {{{theta}}} = 210°  OR  {{{theta}}} = 330°.

<U>Answer</U>.  {{{theta}}} = 210°  OR  {{{theta}}} = 330°.
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