Simplify 1/(2tan(x)(cos(x)^2))

$\frac{1}{2 \tan (x) (\cos^{2} (x))}$

Step 1

Separate fractions.

$\frac{1}{2 (\cos^{2} (x))} \cdot \frac{1}{\tan (x)}$

Step 2

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

$\frac{1}{2 (\cos^{2} (x))} \cdot \frac{1}{\frac{\sin (x)}{\cos (x)}}$

Step 3

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

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

Step 4

Write $1$ as a fraction with denominator $1$ .

$\frac{1}{2 (\cos^{2} (x))} (\frac{1}{1} \cdot \frac{\cos (x)}{\sin (x)})$

Step 5

Simplify.

Rewrite the expression.

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

Multiply $\frac{\cos (x)}{\sin (x)}$ by $1$ .

$\frac{1}{2 (\cos^{2} (x))} \cdot \frac{\cos (x)}{\sin (x)}$

Step 6

Combine.

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

Step 7

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

Factor $\cos (x)$ out of $1 \cos (x)$ .

$\frac{\cos (x) \cdot 1}{2 (\cos^{2} (x)) \sin (x)}$

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 8

Separate fractions.

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

Step 9

Convert from $\frac{1}{\cos (x)}$ to $\sec (x)$ .

$\frac{1}{2 \sin (x)} \sec (x)$

Step 10

Separate fractions.

$\frac{1}{2} \cdot \frac{1}{\sin (x)} \sec (x)$

Step 11

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

$\frac{1}{2} \csc (x) \sec (x)$

Step 12

Combine to $c s c (2 x)$ .

$\csc (2 x)$

Simplify 1/(2tan(x)(cos(x)^2))

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