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`

(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 B

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

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

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

cot A+cot B+cot C+(cos(A+B+C))/(sin A sin B sin C)=

Prove that: a) sin(A+B+C) + sin(A-B-C)+sin(A+B-C) + sin(A-B+C) = 4sinAcosBcosC b) cos(A+B+C)+cos(A+B-C)+cos(B+C-A)+cos(C+A-B)=4cosAcosBcosC

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

Prove that a cos A + b cos B + c cos C = 4R sin A sin B sin C

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