<s>[INST] How to express a trigonometic equation in $\sin 2\theta $ and $\cos 2\theta $? How do I express the given equation in $\sin 2\theta $ and $\cos 2\theta $ in terms of x?
$x + 3 = 7\sin \theta $  with  $\frac{\pi }{2}{\text{ < }}\theta {\text{ < }}\pi $ 
for $\sin 2\theta $ i got $\frac{{( - 2x + 6)\sqrt { - {x^2} - 6x + 40} }}{7}$
for $\cos 2\theta $ i got $\frac{{ - 12x - 49}}{{49}}$
i think im missing something, can someone double check
 [/INST] HINT: $\sin(2\theta) = 2\sin(\theta)\cos(\theta)$
$\cos(2\theta) = \cos^2(\theta) - \sin^2(\theta)$
$\cos^2(\theta) + \sin^2(\theta) = 1$
$\frac{\pi}{2} < \theta < \pi$
$\cos(\theta) < 0$
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