Is the derivation of the following trigonometric identity correct? I accept the conclusion is true and the author reached the correct equation, but look at the 2nd to last line of the page I scanned in (I put a small arrow at the beginning of that line). It reads:

> 
> But $a^2 = \sin^2(x)$, and $b^2 = \cos^2(x)$.
> 
> 
> 

It should read: 

> 
> But $a^2 = \cos^2(x)$, and $b^2 = \sin^2(x)$.
> 
> 
> 

If you look at the 4th and 5th lines from the bottom of the scanned in page it. They are correct, but upon squaring the trig functions the author appears to have swapped around the $a^2$ and the $b^2$. Am I right in this assertion of mine?

The book this came from is "Theta Mathematics" by David Barton, page 156 published by Pearson 2011. This is not homework, I study maths for my own interest.

![enter image description here](https://i.stack.imgur.com/dxtxU.png)