Prove that
`|{:(cos(A-P),cos(A-Q),cos(A-R)),(cos(B-P),cos(B-Q),cos(B-R)),(cos(C-P),cos(C-Q),cos(C-R)):}|`=0.

For all values of A ,B ,Ca n dP ,Q ,R show that |"cos"(A-P)"cos"(A-Q)"cos"(A-R)"cos"(B-P)"cos"(B-Q)"cos"(B-R)"cos"(C-P)"cos"(C-Q)"cos"(C-R)|=0

Prove that: cos(A+B+C)+cos(A-B+C)+cos(A+B-C)+cos(-A+B+C)=4cos A\ cos B\ cos C

Prove that: sin(B-C)cos(A-D) + sin(C-A) cos (B-D) + sin(A-B) cos(C-D) = 0

|(1,cos(A-B), cos(A-C)),(cos(B-A), 1, cos(B-C)),(cos(C-A), cos(C-B), 1)| (A) 0 (B) 1 (C) cosAcosBcosC (D) none of these

Prove that: ("sin"(A-B))/(cos A cosB)+(sin(B-C))/(cos B cos C)+("sin"(C-A))/(cos C cos A)=0

Prove that (sin(B-C))/(cos B cos C)+(sin(C-A))/(cos C cos A)+(sin(A-B))/(cos A cos B)=0

Prove that (sin(B-C))/(cos B cos C)+(sin(C-A))/(cos C cos A)+(sin(A-B))/(cos A cos B)=0

Prove that : acosB\ cos C+bcosCcosA+c\ cos AcosB=/R

Prove that: (cos(A+B+C)+cos(-A+B+C)+cos(A-B+C)+"cos"(A+B-C))/(sin(A+B+C)+sin(-A+B+C)+sin(A-B+C)-"sin"(A+B-C))=cot C

In triangle ABC, prove that cos(A/2)+cos(B/2)+cos(C/2)=4cos(pi-A)/4cos(pi-B)/4cos(pi-C)/4