Question 341689
<pre><b>
{{{Sin(x) = Cos(2x)}}}

Use the identity {{{Cos(2theta)=1-2Sin^2theta}}} on the right side:

{{{Sin(x)=1-2Sin^2x}}}

{{{2Sin^2x+Sin(x)-1=0}}}

The left side factors just like {{{2y^2+y-1}}} factors as {{{(2y-1)(y+1)}}}

{{{(2Sin(x)-1)(Sin(x)+1)=0}}}

Set each factor = 0

Setting the first factor = 0

{{{2Sin(x)-1=0}}}
{{{2Sin(x)=1}}}
{{{Sin(x)=1/2}}}
{{{x="30°;150°"}}}

Setting the second factor = 0

{{{Sin(x)+1=0}}}
{{{Sin(x)=-1}}}
{{{x="270°"}}}

So there are 3 solutions in degrees between 0° and 360°.

Edwin</pre>