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Given that sin(theta) = (x² - y²)/(x² + y²) with theta in (0, 90 deg), determine cos(theta) and cot(theta).

1. cos(theta) = 2xy/(x² + y²), cot(theta) = 2xy/(x² - y²)
2. cos(theta) = (x² + y²)/(2xy), cot(theta) = (x² - y²)/(2xy)
3. cos(theta) = 2xy/(x² + y²), cot(theta) = (x² - y²)/(2xy)
4. cos(theta) = (x² - y²)/(2xy), cot(theta) = 2xy/(x² + y²)

Correct answer: cos(theta) = 2xy/(x² + y²), cot(theta) = 2xy/(x² - y²)

Solution

1 - sin² = 4x² y²/(x²+y²)², so cos = 2xy/(x²+y²); then cot = cos/sin = 2xy/(x² - y²).

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