The value of (sin30° + tan45° − cosec60°)/(sec30° + cos60° + cot45°) is:

Substituting the standard values, the numerator is 1/2 + 1 − 2/√3 and the denominator is 2/√3 + 1/2 + 1. Multiplying both by 2√3 turns the quotient into (3√3 − 4)/(3√3 + 4), and rationalising with the conjugate 3√3 − 4 gives (27 − 24√3 + 16)/(27 − 16) = (43 − 24√3)/11 ≈ 0.130. Rationalising with the wrong conjugate gives (43 + 24√3)/11 ≈ 7.69, flipping the subtraction gives ≈ −0.130, and the two brackets are not equal — they differ in the sign of 2/√3 — so the value is not 1.