Simplify (cot(pi/2-x)sec(x))/(sec(x)^2)

$\frac{\cot (\frac{π}{2} - x) \sec (x)}{\sec^{2} (x)}$

Step 1

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

Factor $\sec (x)$ out of $\cot (\frac{π}{2} - x) \sec (x)$ .

$\frac{\sec (x) \cot (\frac{π}{2} - x)}{\sec^{2} (x)}$

Cancel the common factors.

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

$\frac{\sec (x) \cot (\frac{π}{2} - x)}{\sec (x) \sec (x)}$

Cancel the common factor.

$\frac{\sec (x) \cot (\frac{π}{2} - x)}{\sec (x) \sec (x)}$

Rewrite the expression.

$\frac{\cot (\frac{π}{2} - x)}{\sec (x)}$

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

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