Simplify (cos(x))/(1-tan(x))+(sin(x))/(1-cot(x))

Solve Math

Trigonometry

$\frac{\cos (x)}{1 - \tan (x)} + \frac{\sin (x)}{1 - \cot (x)}$

Simplify each term.

Tap for more steps...

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

$\frac{\cos (x)}{1 - \frac{\sin (x)}{\cos (x)}} + \frac{\sin (x)}{1 - \cot (x)}$

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

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

To write $\frac{\cos (x)}{1 - \frac{\sin (x)}{\cos (x)}}$ as a fraction with a common denominator, multiply by $\frac{1 - \frac{\cos (x)}{\sin (x)}}{1 - \frac{\cos (x)}{\sin (x)}}$ .

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

To write $\frac{\sin (x)}{1 - \frac{\cos (x)}{\sin (x)}}$ as a fraction with a common denominator, multiply by $\frac{1 - \frac{\sin (x)}{\cos (x)}}{1 - \frac{\sin (x)}{\cos (x)}}$ .

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

Write each expression with a common denominator of $(1 - \frac{\sin (x)}{\cos (x)}) (1 - \frac{\cos (x)}{\sin (x)})$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Combine.

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

Combine.

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

Reorder the factors of $(1 - \frac{\sin (x)}{\cos (x)}) (1 - \frac{\cos (x)}{\sin (x)})$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Tap for more steps...

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

$\frac{\cos (x) (1 - \cot (x)) + \sin (x) (1 - \frac{\sin (x)}{\cos (x)})}{(1 - \frac{\cos (x)}{\sin (x)}) (1 - \frac{\sin (x)}{\cos (x)})}$

Apply the distributive property.

$\frac{\cos (x) \cdot 1 + \cos (x) (- \cot (x)) + \sin (x) (1 - \frac{\sin (x)}{\cos (x)})}{(1 - \frac{\cos (x)}{\sin (x)}) (1 - \frac{\sin (x)}{\cos (x)})}$

Multiply $\cos (x)$ by $1$ .

$\frac{\cos (x) + \cos (x) (- \cot (x)) + \sin (x) (1 - \frac{\sin (x)}{\cos (x)})}{(1 - \frac{\cos (x)}{\sin (x)}) (1 - \frac{\sin (x)}{\cos (x)})}$

Rewrite using the commutative property of multiplication.

$\frac{\cos (x) - \cos (x) \cot (x) + \sin (x) (1 - \frac{\sin (x)}{\cos (x)})}{(1 - \frac{\cos (x)}{\sin (x)}) (1 - \frac{\sin (x)}{\cos (x)})}$

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

$\frac{\cos (x) - \cos (x) \cot (x) + \sin (x) (1 - \tan (x))}{(1 - \frac{\cos (x)}{\sin (x)}) (1 - \frac{\sin (x)}{\cos (x)})}$

Apply the distributive property.

$\frac{\cos (x) - \cos (x) \cot (x) + \sin (x) \cdot 1 + \sin (x) (- \tan (x))}{(1 - \frac{\cos (x)}{\sin (x)}) (1 - \frac{\sin (x)}{\cos (x)})}$

Multiply $\sin (x)$ by $1$ .

$\frac{\cos (x) - \cos (x) \cot (x) + \sin (x) + \sin (x) (- \tan (x))}{(1 - \frac{\cos (x)}{\sin (x)}) (1 - \frac{\sin (x)}{\cos (x)})}$

Rewrite using the commutative property of multiplication.

$\frac{\cos (x) - \cos (x) \cot (x) + \sin (x) - \sin (x) \tan (x)}{(1 - \frac{\cos (x)}{\sin (x)}) (1 - \frac{\sin (x)}{\cos (x)})}$

Simplify the denominator.

Tap for more steps...

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

$\frac{\cos (x) - \cos (x) \cot (x) + \sin (x) - \sin (x) \tan (x)}{(1 - \cot (x)) (1 - \frac{\sin (x)}{\cos (x)})}$

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

$\frac{\cos (x) - \cos (x) \cot (x) + \sin (x) - \sin (x) \tan (x)}{(1 - \cot (x)) (1 - \tan (x))}$

Do you know how to Simplify (cos(x))/(1-tan(x))+(sin(x))/(1-cot(x))? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Find the Quadrant of the Angle 70.9 degrees

Solve for x cos(x)csc(x)tan(x)=1

Graph 2sin(x)^2+7sin(x)=3

Graph y=x^(5/2)

Find the Exact Value arcsec(6)