[Calculus II] Integral of sin5x/cos^2(5x)

https://gyazo.com/3267112f63009e4c50e1e0b27f841628

So, the original integral is sin(5x)/cos^2(5x), then Pearson says I replace sin(5x)/cos(5x) with a ratio identity, as if cos^2(5x) was never raised to the second power. How is this possible?