Question

tan(x/2)=(sinx)/1+cosx for all values of x
true or false

Answer 1

sinx=2sinx/2 cosx/2........1
1+cosx=2(cosx)^2............2
1/2=tan(x/2).....
seems to be right!!!!!

Answer 2

1+cosx=2*(cosx/2)^2
edit it while doing....

Answer 3

\[\sin(x)/(1+\cos(x))=\sin(2(x/2))/(1+\cos(2(x/2))=\]
\[2\sin(x/2)\cos(x/2)/(1+\cos^2(x/2)-\sin^2(x/2))=\]
\[2\sin(x/2)\cos(x/2)/(\sin^2(x/2)+\cos^2(x/2)+\cos^2(x/2)-\sin^2(x/2))=\]
\[\frac{2\sin(x/2)\cos(x/2)}{2\cos^2(x/2)}=\frac{\sin(x/2)}{\cos(x/2)}=\tan(x/2)\]
Using the identities:
\[\sin(2x)=2\sin(x)\cos(x); \cos(2x)=\cos^2(x)-\sin^2(x); \cos^2(x)+\sin^2(x)=1\]