I forgot to study for Finals anybody know AP Trigonometry? If x+y+z=\pix+y+z=π prove the trigonometric identity
cot{\frac{x}{2}}+cot{\frac{y}{2}}+c otg\frac{z}{2}=cot{\frac{x}{2}}cot{ \frac{y}{2}}cot{\frac{z}{2}}cot
x+y+z=π, so \{\frac{x}{2}}+{\frac{y}{2}}={\frac {\pi}{2}}-{\frac{z}{2}}; {\frac{z}{2}}={\frac{\pi}{2}}-({\fr ac{x}{2}}+{\frac{y}{2}})

). Because of \displaystyle cot\alpha={\frac{1}{tan\alpha}}cotα =
, we get \displaystyle cot\alpha={\frac{cos\alpha}{sin\alp ha}}cotα=
sinα
cosα
. Then \displaystyle cot{\frac{x}{2}}+cot{\frac{y}{2}}+c ot{\frac{z}{2}}={\frac{cos{\frac{x} {2}}}{sin{\frac{x}{2+{\frac{cos{\fr ac{y}{2}}}{sin{\frac{y}{2+{\frac{co s{\frac{z}{2}}}{sin{\frac{z}{2={\fr ac{cos{\frac{x}{2}}sin{\frac{y}{2}} +cos{\frac{y}{2}}sin{\frac{x}{2}}}{ sin{\frac{x}{2}}sin{\frac{y}{2+{\fr ac{cos{\frac{z}{2}}}{sin{\frac{z}{2 ={\frac{sin({\frac{x}{2}}+{\frac{y} {2}})}{sin{\frac{x}{2}}sin{\frac{y} {2+{\frac{cos{\frac{z}{2}}}{sin{\fr ac{z}{2={\frac{cos{\frac{z}{2}}}{si n{\frac{x}{2}}sin{\frac{y}{2+{\frac {cos{\frac{z}{2}}}{sin{\frac{z}{2=c os{\frac{z}{2}}\cdot{\frac{sin{\fra c{z}{2}}+sin{\frac{x}{2}}sin{\frac{ y}{2}}}{sin{\frac{x}{2}}sin{\frac{y }{2}}sin{\frac{z}{2={\frac{cos{\fra c{z}{2}}}{sin{\frac{z}{2\cdot{\frac {cos({\frac{x}{2}}+{\frac{y}{2}})+s in{\frac{x}{2}}sin{\frac{y}{2}}}{si n{\frac{x}{2}}sin{\frac{y}{2={\frac {cos{\frac{z}{2}}}{sin{\frac{z}{2\c dot{\frac{cos{\frac{x}{2}}cos{\frac {y}{2}}}{sin{\frac{x}{2}}sin{\frac{ y}{2=cot{\frac{x}{2}}cot{\frac{y}{2 }}cot{\frac{z}{2}}cot
+cot
2
z
=