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**skeeter** 1. $\displaystyle \sin(4x)=-2\sin(2x)$

$\displaystyle 2\sin(2x)\cos(2x) + 2\sin(2x) = 0$

$\displaystyle 2\sin(2x)[\cos(2x) + 1] = 0$

set each factor equal to 0 and solve.

2. $\displaystyle [\sin(2x)+\cos(2x)]^2=0$

$\displaystyle \sin(2x) + \cos(2x) = 0$

$\displaystyle \sin(2x) = -\cos(2x)$

for what angles do cosine and sine have opposite values?

3. $\displaystyle 2\sin(2x)=-\tan(2x)$

$\displaystyle 2\sin(2x) + \tan(2x) = 0$

$\displaystyle \sin(2x)[2 + \sec(2x)] = 0$

set each factor equal to 0 and solve.