Find transformer leakage reactance
Both the answers are right.

There are many instances where my answer and the solution manual's answer are different by &lt; 0.1% as in this case.

Coming to the reasoning part, the cos(phi) term given is the R(phase) / Z(phase).

where Z(phase) = sqrt((R(phase))^2 + (X(phase))^2).

As cos(phi) = sqrt(2) / 2, tan(phi) = 1 = R(phase) / X(phase).
Hence X(phase) = R(phase).

So your answer and the manual's answer are correct, and your answer is a bit more accurate.