数学三角函数恒等变化怎么用只含有半角的正切的式子分别表示角的正弦、余弦和正切,

sin2x=2sinxcosx=2tanxcos^2 x;
cos2x=cos^2 x-sin^2 x=(1-tan^x)cos^2 x;
两个式子相除，tan2x=2tanx/(1-tan^2 x);
cos^2 x=1(tan^2 x+1)，代入
前两个式子，得出。。。然后将2x看成x，等号右边的就是x/2咯

sinx=2sin(x/2)cos(x/2)=2tan(x/2)cos^2(x /2);
cosx=cos^2(x /2)-sin^2 (x /2)=(1-tan^2(x /2))cos^2 (x /2);
tanx=2tan(x /2)/(1-tan^2 (x /2));
cos^2(x /2)+sin^2 (x /2)=1;
1+tan^2 (x /2))=1/cos^2 (x /2);
故cos^2(x /2)=1/(tan^2(x /2)+1),代入
得sinx=2tan(x/2)cos^2(x /2)=2tan(x/2)/(tan^2(x /2)+1)
cosx=(1-tan^2(x /2))cos^2 (x /2)=(1-tan^2(x /2))/(tan^2(x /2)+1)
cotx=1/tanx=(1-tan^2 (x /2))/(2tan(x /2))