Least common denominator (sin(2*x)/2+x)/2

You have entered [src]

sin(2*x)    
-------- + x
   2        
------------
     2

$$\frac{x + \frac{\sin{\left(2 x \right)}}{2}}{2}$$

(sin(2*x)/2 + x)/2

General simplification [src]

x   sin(2*x)
- + --------
2      4

$$\frac{x}{2} + \frac{\sin{\left(2 x \right)}}{4}$$

x/2 + sin(2*x)/4

Trigonometric part [src]

       /      pi\
    cos|2*x - --|
x      \      2 /
- + -------------
2         4

$$\frac{x}{2} + \frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{4}$$

x          1       
- + ---------------
2        /      pi\
    4*sec|2*x - --|
         \      2 /

$$\frac{x}{2} + \frac{1}{4 \sec{\left(2 x - \frac{\pi}{2} \right)}}$$

x        tan(x)    
- + ---------------
2     /       2   \
    2*\1 + tan (x)/

$$\frac{x}{2} + \frac{\tan{\left(x \right)}}{2 \left(\tan^{2}{\left(x \right)} + 1\right)}$$

x   sin(2*x)
- + --------
2      4

$$\frac{x}{2} + \frac{\sin{\left(2 x \right)}}{4}$$

x        cot(x)    
- + ---------------
2     /       2   \
    2*\1 + cot (x)/

$$\frac{x}{2} + \frac{\cot{\left(x \right)}}{2 \left(\cot^{2}{\left(x \right)} + 1\right)}$$

x       1     
- + ----------
2   4*csc(2*x)

$$\frac{x}{2} + \frac{1}{4 \csc{\left(2 x \right)}}$$

x/2 + 1/(4*csc(2*x))

Common denominator [src]

x   sin(2*x)
- + --------
2      4

$$\frac{x}{2} + \frac{\sin{\left(2 x \right)}}{4}$$

x/2 + sin(2*x)/4

Combining rational expressions [src]

2*x + sin(2*x)
--------------
      4

$$\frac{2 x + \sin{\left(2 x \right)}}{4}$$

(2*x + sin(2*x))/4

Expand expression [src]

x   cos(x)*sin(x)
- + -------------
2         2

$$\frac{x}{2} + \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{2}$$

x/2 + cos(x)*sin(x)/2

Assemble expression [src]

x   sin(2*x)
- + --------
2      4

$$\frac{x}{2} + \frac{\sin{\left(2 x \right)}}{4}$$

x/2 + sin(2*x)/4

Powers [src]

x   sin(2*x)
- + --------
2      4

$$\frac{x}{2} + \frac{\sin{\left(2 x \right)}}{4}$$

      /   -2*I*x    2*I*x\
x   I*\- e       + e     /
- - ----------------------
2             8

$$\frac{x}{2} - \frac{i \left(e^{2 i x} - e^{- 2 i x}\right)}{8}$$

x/2 - i*(-exp(-2*i*x) + exp(2*i*x))/8

Combinatorics [src]

x   sin(2*x)
- + --------
2      4

$$\frac{x}{2} + \frac{\sin{\left(2 x \right)}}{4}$$

x/2 + sin(2*x)/4

Rational denominator [src]

2*x + sin(2*x)
--------------
      4

$$\frac{2 x + \sin{\left(2 x \right)}}{4}$$

(2*x + sin(2*x))/4

Numerical answer [src]

0.25*sin(2*x) + 0.5*x

0.25*sin(2*x) + 0.5*x