Mathematical high school expansion

The expansion of that part

Triangle:

Common identities in triangles

1，tanAtanBtanC=tanA+tanB+tanC

2，tannA+tannB+tannC = tan(nA)tan(nB)tan(nC)，

3、cot(nA/2)+cot(nB/2)+cot(nC/2)= cot(nA/2)* cot(nB/2)* cot(nC/2)

4、cot(nA)* cot(nB)+cot(nA)* cot(nC)+cot(nB)* cot(nC)= 1，

5, tan (na/2) tan (nb/2)+tan (nb/2) tan (NC/2)+tan (na/2) tan (NC/2) =1,(n is an odd number).

6. SIN (Na)+SIN (NB)+SIN (NC) = 4 SIN (nπ/2) * COS (Na/2) * COS (NB/2) * COS (NC/2), (n is an odd number).

7. sin (na)+sin (nb)+sin (NC) = 4cos (nπ/2) * sin (na/2) * sin (nb/2) * sin (NC/2), (n is an even number).

8. COS (Na)+COS (NB)+COS (NC) =1+4Sin (nπ/2) * SIN (Na/2) * SIN (NB/2) * SIN (NC/2), (N is an odd number).

9. COS (Na)+COS (NB)+COS (NC) =-1+4cos (nπ/2) * COS (Na/2) * COS (NB/2) * COS (NC/2), (n is an even number).

10，sin(A/2)+sin(B/2)+sin(C/2)= 1+4 sin[(π-A)/4]sin[(π-B)/4]sin[(π-C)/4]，

1 1，cos(A/2)+cos(B/2)+cos(C/2)= 4 cos[(π-A)/4]cos[(π-B)/4]cos[(π-C)/4]，

12,(sina)^2+(sinb)^2+(sinc)^2=2+2cosacosbcos

13,,(cosa)^2+(cosb)^2+(cosc)^2= 1-2cosacosbcosc

In the vector, the related fixed point and three-point * * * line problems are calculated by Menelaus theorem.

Robida's law in derivatives, etc.