Write the Fraction in Simplest Form (tan(pi/2-x)csc(x))/(csc(x)^2)

$\frac{\tan (\frac{π}{2} - x) \csc (x)}{\csc^{2} (x)}$

Step 1

Cancel the common factor of $\csc (x)$ and $\csc^{2} (x)$ .

Factor $\csc (x)$ out of $\tan (\frac{π}{2} - x) \csc (x)$ .

$\frac{\csc (x) \tan (\frac{π}{2} - x)}{\csc^{2} (x)}$

Cancel the common factors.

Factor $\csc (x)$ out of $\csc^{2} (x)$ .

$\frac{\csc (x) \tan (\frac{π}{2} - x)}{\csc (x) \csc (x)}$

Cancel the common factor.

$\frac{\csc (x) \tan (\frac{π}{2} - x)}{\csc (x) \csc (x)}$

Rewrite the expression.

$\frac{\tan (\frac{π}{2} - x)}{\csc (x)}$

Step 2

Rewrite $\csc (x)$ in terms of sines and cosines.

$\frac{\tan (\frac{π}{2} - x)}{\frac{1}{\sin (x)}}$

Step 3

Rewrite $\tan (\frac{π}{2} - x)$ in terms of sines and cosines.

$\frac{\frac{\sin (\frac{π}{2} - x)}{\cos (\frac{π}{2} - x)}}{\frac{1}{\sin (x)}}$

Step 4

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\sin (x)}$ .

$\frac{\sin (\frac{π}{2} - x) \sin (x)}{\cos (\frac{π}{2} - x)}$

Step 5

Convert from $\frac{\sin (\frac{π}{2} - x) \sin (x)}{\cos (\frac{π}{2} - x)}$ to $\sin (\frac{π}{2} - x) \tan (\frac{π}{2} - x)$ .

$\sin (\frac{π}{2} - x) \tan (\frac{π}{2} - x)$