Exact Reciprocal Values

At 30°, 45° and 60° the reciprocal ratios are exact too: flip the value from the table, then tidy the root.

csc(30°) is 1/(1/2), which is 2. sec(45°) is 1/(√2/2), which is 2/√2, or √2. cot(60°) is 1/√3, which is √3/3. So sec(60°) + csc(30°) is 2 + 2, which is 4, with no decimals anywhere.

Squares work the same way: square the value, and the root disappears. (√3)² is 3 and (√2)² is 2.