Question 1008640
<pre>
{{{2-2cos^2(x)=-3sin(x)-1}}}

Add 1 to both sides:

{{{3-2cos^2(x)=-3sin(x)}}}

Use the identity {{{sin^2(theta)+cos^2(theta)=1}}} solved for cos<sup>2</sup>(<font face="symbol">q</font>)

{{{3-2(1-sin^2(x)^"")=-3sin(x)}}}

{{{3-2+2sin^2(x)=-3sin(x)}}}

{{{1+2sin^2(x)=-3sin(x)}}}

Get 0 on the right side

{{{2sin^2(x)+3sin(x)+1=0}}}

Factor the left side as a quadratic in sin(x)

{{{(2sin(x)^""+1^"")(sin(x)^""+1^"")=0}}}

Use the zero-factor property:

{{{2sin(x)+1=0}}};   {{{sin(x)+1=0}}}

{{{2sin(x)=-1}}};    {{{sin(x)=-1}}}

{{{sin(x)=-1/2}}};     {{{x=3pi/2}}}

{{{x=7pi/6}}};{{{11pi/6}}}   

These are the solutions for {{{0<=x<2pi}}}.
To get all solutions add {{{2pi*n}}} to them.

Edwin</pre>