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KiRa [710]
2 years ago
11

Determine an exact value for sin _ 3π/4-tan 5π/6

Mathematics
1 answer:
iris [78.8K]2 years ago
6 0

Answer:

\frac{3\sqrt{2}+2\sqrt{3}}{6} or \frac{\sqrt{2}}{2}+\frac{\sqrt{3}}{3}

Step-by-step explanation:

\sin\frac{3\pi}{4}-\tan\frac{5\pi}{6}\\\\\sin\frac{3\pi}{4}-\frac{\sin\frac{5\pi}{6}}{\cos\frac{5\pi}{6}}\\ \\\frac{\sqrt{2}}{2}-\frac{\frac{1}{2} }{-\frac{\sqrt{3}}{2}}\\ \\\frac{\sqrt{2}}{2}+\frac{1}{\sqrt{3}}\\ \\\frac{\sqrt{2}}{2}+\frac{\sqrt{3}}{3}\\ \\\frac{3\sqrt{2}}{6}+\frac{2\sqrt{3}}{6}\\ \\\frac{3\sqrt{2}+2\sqrt{3}}{6}

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