<p>Could someone please help me solve the following:</p>
<p>cos2x - sin2x = 0</p>
<p>Thanks!</p>
<p>You cant really solve that unless you have an interval. Otherwise the solutions would be endless.</p>
<p>Interval is [0,2 pi)</p>
<p>let's assume x is in degrees</p>
<p>therefore cos2x = sin(90-2x)
so sin(90-2x) = sin2x
hence 90-2x = 2x
=> 4x = 90
=> x = 22.5 degrees!</p>
<p>that's it! hope this helps.</p>
<p>22.5 degrees is also equal to pi/8 rad.</p>
<p>cos(2x) = sin(2x)
cos^2(2x) = sin^2(2x)
1 - sin^2(2x) = sin^2(2x)
sin^2(2x) = 1/2
sin(2x) = sqrt(2)/2
2x = pi/4 or 2x = 3pi/4 (this answer doesn't work since we squared both sides)
x = pi/8</p>
<p>the solution is for the specified interval: {x: 0 < x < 360 degrees}</p>
<p>Thank you guys so much!</p>