Your work is absolutely correct!
. . The book did something really stupid!
Their answer is correct . . . but unforgivably stupid!
You had: .
Consider the right triangle:
Since , we have: .
* | ________
5x * | √25x² - 1
* θ |
* - - - - - - - - *
Using Pythagorus, we find that: .
Since , it is true that
. . but it is a truly silly way to write the answer!
By their reasoning, all of these are also correct answers:
but who (in their right minds) would insist on using them?