Mister Exam

# Least common denominator atan(tan(f)*sqrt(a^2-1)/a)/sqrt(a^2-1)

An expression to simplify:

### The solution

You have entered [src]
    /          ________\
|         /  2     |
|tan(f)*\/  a  - 1 |
atan|------------------|
\        a         /
------------------------
________
/  2
\/  a  - 1        
$$\frac{\operatorname{atan}{\left(\frac{\sqrt{a^{2} - 1} \tan{\left(f \right)}}{a} \right)}}{\sqrt{a^{2} - 1}}$$
atan((tan(f)*sqrt(a^2 - 1))/a)/sqrt(a^2 - 1)
Trigonometric part [src]
    /   _________       \
|  /       2        |
|\/  -1 + a  *sec(f)|
atan|-------------------|
|        /    pi\   |
|   a*sec|f - --|   |
\        \    2 /   /
-------------------------
_________
/       2
\/  -1 + a        
$$\frac{\operatorname{atan}{\left(\frac{\sqrt{a^{2} - 1} \sec{\left(f \right)}}{a \sec{\left(f - \frac{\pi}{2} \right)}} \right)}}{\sqrt{a^{2} - 1}}$$
    /   _________            \
|  /       2     /pi    \|
|\/  -1 + a  *csc|-- - f||
|                \2     /|
atan|------------------------|
\        a*csc(f)        /
------------------------------
_________
/       2
\/  -1 + a           
$$\frac{\operatorname{atan}{\left(\frac{\sqrt{a^{2} - 1} \csc{\left(- f + \frac{\pi}{2} \right)}}{a \csc{\left(f \right)}} \right)}}{\sqrt{a^{2} - 1}}$$
    /   _________       \
|  /       2        |
|\/  -1 + a  *sin(f)|
atan|-------------------|
\      a*cos(f)     /
-------------------------
_________
/       2
\/  -1 + a        
$$\frac{\operatorname{atan}{\left(\frac{\sqrt{a^{2} - 1} \sin{\left(f \right)}}{a \cos{\left(f \right)}} \right)}}{\sqrt{a^{2} - 1}}$$
    /   _________\
|  /       2 |
|\/  -1 + a  |
atan|------------|
\  a*cot(f)  /
------------------
_________
/       2
\/  -1 + a     
$$\frac{\operatorname{atan}{\left(\frac{\sqrt{a^{2} - 1}}{a \cot{\left(f \right)}} \right)}}{\sqrt{a^{2} - 1}}$$
    /   _________       \
|  /       2        |
|\/  -1 + a  *sec(f)|
atan|-------------------|
\      a*csc(f)     /
-------------------------
_________
/       2
\/  -1 + a        
$$\frac{\operatorname{atan}{\left(\frac{\sqrt{a^{2} - 1} \sec{\left(f \right)}}{a \csc{\left(f \right)}} \right)}}{\sqrt{a^{2} - 1}}$$
    /   _________            \
|  /       2     /    pi\|
|\/  -1 + a  *cos|f - --||
|                \    2 /|
atan|------------------------|
\        a*cos(f)        /
------------------------------
_________
/       2
\/  -1 + a           
$$\frac{\operatorname{atan}{\left(\frac{\sqrt{a^{2} - 1} \cos{\left(f - \frac{\pi}{2} \right)}}{a \cos{\left(f \right)}} \right)}}{\sqrt{a^{2} - 1}}$$
    /     _________        \
|    /       2     2   |
|2*\/  -1 + a  *sin (f)|
atan|----------------------|
\      a*sin(2*f)      /
----------------------------
_________
/       2
\/  -1 + a          
$$\frac{\operatorname{atan}{\left(\frac{2 \sqrt{a^{2} - 1} \sin^{2}{\left(f \right)}}{a \sin{\left(2 f \right)}} \right)}}{\sqrt{a^{2} - 1}}$$
atan(2*sqrt(-1 + a^2)*sin(f)^2/(a*sin(2*f)))/sqrt(-1 + a^2)
Combinatorics [src]
    /   _________       \
|  /       2        |
|\/  -1 + a  *tan(f)|
atan|-------------------|
\         a         /
-------------------------
__________________
\/ (1 + a)*(-1 + a)   
$$\frac{\operatorname{atan}{\left(\frac{\sqrt{a^{2} - 1} \tan{\left(f \right)}}{a} \right)}}{\sqrt{\left(a - 1\right) \left(a + 1\right)}}$$
atan(sqrt(-1 + a^2)*tan(f)/a)/sqrt((1 + a)*(-1 + a))
(-1.0 + a^2)^(-0.5)*atan((tan(f)*sqrt(a^2 - 1))/a)
(-1.0 + a^2)^(-0.5)*atan((tan(f)*sqrt(a^2 - 1))/a)
Powers [src]
    /     _________                 \
|    /       2  /   I*f    -I*f\|
|I*\/  -1 + a  *\- e    + e    /|
atan|-------------------------------|
|          / I*f    -I*f\       |
\        a*\e    + e    /       /
-------------------------------------
_________
/       2
\/  -1 + a              
$$\frac{\operatorname{atan}{\left(\frac{i \sqrt{a^{2} - 1} \left(- e^{i f} + e^{- i f}\right)}{a \left(e^{i f} + e^{- i f}\right)} \right)}}{\sqrt{a^{2} - 1}}$$
atan(i*sqrt(-1 + a^2)*(-exp(i*f) + exp(-i*f))/(a*(exp(i*f) + exp(-i*f))))/sqrt(-1 + a^2)