# Math Help - trigonometric identiy

1. ## trigonometric identiy

how would simply/solve (1+cosx)/(sinx) + (sinx)/(1+cosx)?

2. $\frac{1+cosx}{sinx}+\frac{sinx}{1+cosx}$

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

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

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

3. Originally Posted by Amer
$\frac{1+cosx}{sinx}+\frac{sinx}{1+cosx}$

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

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

$\frac{1+2cosx}{sinx(1+cosx)}$
Minor correction: the last step should be

$\frac{{\color{red}2}+2cosx}{sinx(1+cosx)}$ ,

which means we can simplify further:

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

$\frac{2}{sinx}$

$2csc\ x$

01

4. Thanks very much I forget it

5. thank you guys so much