26. (sin²x + cos²x) / sin x (1 - cos²x + 1 - sin²x) / sin x

Explanation:

Step1: Use trigonometric identity

Recall that $\sin^{2}x+\cos^{2}x = 1$. So the original expression $\frac{\sin^{2}x+\cos^{2}x}{\sin x}$ becomes $\frac{1}{\sin x}$. The second - line expression $\frac{1 - \cos^{2}x+1-\sin^{2}x}{\sin x}$ simplifies as follows: Since $\sin^{2}x+\cos^{2}x = 1$, then $1-\cos^{2}x=\sin^{2}x$ and $1 - \sin^{2}x=\cos^{2}x$. So $1 - \cos^{2}x+1-\sin^{2}x=\sin^{2}x+\cos^{2}x = 1$. And $\frac{1 - \cos^{2}x+1-\sin^{2}x}{\sin x}=\frac{1}{\sin x}$.

Answer:

$\frac{1}{\sin x}$