Question 806224
<font face="Times New Roman" size="+2">


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4\sin\theta\ -\ 1\ =\ 2\sin\theta]


Square both sides:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 16\sin^2\theta\ -8\sin\theta\ +\ 1\ =\ 4\sin^2\theta]


Collect like terms


Let *[tex \Large u\ =\ \sin\theta] and substitute.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 12u^2\ -\ 8u\ +\ 1]


Solve the factorable quadratic.  Check BOTH answers since one or both may be extraneous caused by squaring.  Then find the inverse sin value(s) of any valid root(s).  Don't forget to add *[tex \Large +\ 2k\pi,\ \  k\ \in\ \mathbb{Z}] to each element of the solution set.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
<div style="text-align:center"><a href="http://outcampaign.org/" target="_blank"><img src="http://cdn.cloudfiles.mosso.com/c116811/scarlet_A.png" border="0" alt="The Out Campaign: Scarlet Letter of Atheism" width="143" height="122" /></a></div>
</font>