<p>This is a review problem... but my brain is fried, and I cannot figure out for the life of me what I'm doing wrong.</p>
<p>Solve sin2x = -cosx for x E R.</p>
<p>(I got to 2sinxcosx=-cosx.)</p>
<p>Someone help please! This should be easy. :(</p>
<p>Divide both sides by cos(x)</p>
<p>It is.</p>
<p>sin(2x) = -cos(x)
sin(2x) = 2sin(x)cos(x)
2sin(x)cos(x) = -cos(x) [Substitution]
2sin(x) = -1
sin(x) = -1/2
x = (7pi)/6 or (11pi)/6</p>
<p>That's why I'm confused... my teacher marked it wrong because you cannot divide by cos(x)-- because cos(x) could equal zero. Hmmmm...</p>
<p>sin(2x) = -cos(x)
2sin(x)cos(x) = -cos(x)
2sin(x)cos(x) + cos(x) = 0
cos(x)[2sin(x)+1] = 0
cos(x) = 0 or sin(x) = -1/2
x = (pi/2) + (2n)pi and x = (7pi/6) + (2n)pi *and<a href="11pi/6">/i</a> + (2n)pi</p>