If sec(t) = x/y, then cot(t) is equal to:

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Given sec(t) = x/y.

Recall that sec(t) = 1/cos(t), so cos(t) = y/x.

Using the Pythagorean identity: sin²(t) + cos²(t) = 1,

sin²(t) = 1 - cos²(t) = 1 - (y/x)² = 1 - y²/x² = (x² - y²)/x².

Therefore, sin(t) = √(x² - y²) / x.

Cotangent is cot(t) = cos(t) / sin(t) = (y/x) / (√(x² - y²)/x) = y / √(x² - y²).

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