Exact Reciprocal Values

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

$\csc\left(30^{\circ}\right)$ is 1/(1/2), which is 2. $\sec\left(45^{\circ}\right)$ is 1/(√2/2), which is 2/√2, or √2. $\cot\left(60^{\circ}\right)$ is 1/√3, which is √3/3. So $\sec\left(60^{\circ}\right)+\csc\left(30^{\circ}\right)$ 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.