<p>Solve
2sinx + cos2x = 2(sinx)^2 - 1 </p>
<p>for 0≤x≤2pi</p>
<p>How do I solve this without a graphing calculator?</p>
<p>cos 2x = 1 - 2 sin^2 (x), so we have</p>
<p>2 sin x + (1 - 2 sin^2(x)) = 2 sin^2 (x) - 1</p>
<p>Let u = sin x, this becomes a quadratic in terms of u. Solve for u. Remember that -1 <= u <= 1, since sin x can only range from -1 to 1, inclusive.</p>