`|(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 |{:(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.

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

If A+B+C=pi, then the value of |[sin(A+B+C),sin(A+C),cosC],[-sinB,0,tanC],[cos(A+B),tan(B+C),0]| is equal to (a) 0 (b) 1 (c) 2sinBtanAcosC (d) none of these

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

(cos(A-B))/(cos(A+B))+cos(C+D)/(cos(C-D))=0 => tan A tan B tan C tan D =

If f,g,h are the internal bisectors of a /_\ ABC then 1/f cos (A/2)+ 1/g cos (B/2) +1/h cos (C/2)= (A) 1/a+1/b-1/c (B) 1/a-1/b+1/c (C) 1/a+1/b+1/c (D) none of these

If cos2B=(cos(A+C))/("cos"(A-C)) , then tanA ,t a n B ,tanC are in (a)A.P. (b) G.P. (c) H.P. (d) none of these