# Thread: calc fundamental identities

1. ## calc fundamental identities

how to simplify

sin X / 1+ cos X + 1+cos X / sin X

2. Originally Posted by sandman69
how do you simplify

sin x / 1+cos x + 1+cos x / sin x
Hi sandman69,

You need a common denominator

$\frac{sinx}{1+cosx}+\frac{1+cosx}{sinx}=\frac{sinx }{sinx}\ \left(\frac{sinx}{1+cosx}\right)+\frac{1+cosx}{1+c osx}\ \left(\frac{1+cosx}{sinx}\right)$

$=\frac{sin^2x}{sinx(1+cosx)}+\frac{1+2cosx+cos^2x} {sinx(1+cosx)}=\frac{sin^2x+cos^2x+1+2cosx}{sinx(1 +cosx)}$

$sin^2x+cos^2x=1$

so we get

$\frac{2+2cosx}{sinx(1+cosx)}=\frac{2(1+cosx)}{sinx (1+cosx)}$

$\frac{1+cosx}{1+cosx}=1$

$\frac{2}{sinx}=2cosecx$

3. Originally Posted by sandman69
how to simplify

sin X /(1+ cos X) + (1+cos X)/sin X
as shown above, please use parentheses to make your trig expression clear ...

$\frac{\sin{x}}{1+\cos{x}} + \frac{1+\cos{x}}{\sin{x}}
$

common denominator is $\sin{x}(1+\cos{x})$ ...

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

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

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

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

$\frac{2}{\sin{x}} = 2\csc{x}$

4. ## fundamental identities

how do you do
(tan x + cot) / (sec * csc)

5. Originally Posted by sandman69
how do you do
(tan x + cot) / (sec * csc)
First things first remove that denominator and convert to $\sin(x)$ and $\cos(x)$

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

For that left term get the same denominator

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

which gives us $\left(\frac{\sin^2(x)+\cos^2(x)}{\cos(x) \sin(x)}\right) \cdot \sin(x)\cos(x) = \sin^2(x) + \cos^2(x)$

You can still cancel that further using a well known identity which you must know .

6. ## fundamental identites

do you know wer i could find alll the rules for these.