Simplify 1/(cot(theta))+1/(tan(theta))

$\frac{1}{\cot (θ)} + \frac{1}{\tan (θ)}$

Step 1

Rewrite $\cot (θ)$ in terms of sines and cosines.

$\frac{1}{\frac{\cos (θ)}{\sin (θ)}} + \frac{1}{\tan (θ)}$

Step 2

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

$\frac{\sin (θ)}{\cos (θ)} + \frac{1}{\tan (θ)}$

Step 3

Convert from $\frac{\sin (θ)}{\cos (θ)}$ to $\tan (θ)$ .

$\tan (θ) + \frac{1}{\tan (θ)}$

Step 4

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

$\tan (θ) + \frac{1}{\frac{\sin (θ)}{\cos (θ)}}$

Step 5

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

$\tan (θ) + \frac{\cos (θ)}{\sin (θ)}$

Step 6

Convert from $\frac{\cos (θ)}{\sin (θ)}$ to $\cot (θ)$ .

$\tan (θ) + \cot (θ)$