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sleet_krkn [62]
4 years ago
11

6cos x-6sin x=3.sqrt6

Mathematics
1 answer:
Yakvenalex [24]4 years ago
7 0
Divide by 6
cos x - sin x = \frac{\sqrt{6}}{2}

Square both sides
cos^2 x -2 sin x cos x + sin^2 x = \frac{3}{2}

Simplify Left side using Trig identities: (Pythagorean, Double Angle)
1 - sin (2x) = \frac{3}{2}

Solve for x:
sin (2x) = -\frac{1}{2}  \\  \\ 2x = \frac{7 \pi}{6}, \frac{11 \pi}{6} \\  \\ x = \frac{7 \pi}{12}, \frac{11 \pi}{12}
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