<s>[INST] Solve: $5\cos^2 (x) - 4\sin (x)\cos (x)+3\sin^2 (x)=2$ Solve to find the general value of $x$:
$$5\cos^2 (x) - 4\sin (x)\cos (x)+3\sin^2 (x)=2$$
My Attempt:
$$5(1-\sin^2 (x))-4\sin (x)\cos (x)+3\sin^2 (x)=2$$
$$5-5\sin^2 (x)-4\sin (x)\cos (x)+3\sin^2 (x)=2$$
$$2\sin^2 (x)+4\sin (x)\cos (x)=3$$
 [/INST] Guide:
$$2\sin^2(x)+4\sin(x)\cos(x)=3$$
$$2\sin(2x)=2+1-2\sin^2(x)$$
$$2\sin(2x) = 2+\cos(2x)$$
$$2\sin(2x)-\cos(2x)=2$$
The trick from here should help in solving the problem.
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