In a triangle, if the angles `A , B ,a n dC` are in A.P. show that `2cos1/2(A-C)=(a+c)/(sqrt(a^2-a c+c^2))`

Show that cos[(B-C)/2]=(b+c)/a sin(A/2)

If a,b,c are in A.P., show that (a-c)^(2)=4(b^(2)-ac) .

If a ,b ,a n dc are in G.P. then prove that 1/(a^2-b^2)+1/(b^2)=1/(b^2-c^2)dot

If A , B and C are interior angles of triangle ABC ,then show that sin ((B+C)/( 2) )=cos (A) /(2)

In a Delta ABC , If tan A/2, tan B/2, tan C/2 are in A.P. then cos A. cos B, cos C are in

a triangle A B C with fixed base B C , the vertex A moves such that cosB+cosC=4sin^2(A/2)dot If a ,ba n dc , denote the length of the sides of the triangle opposite to the angles A , B ,a n dC , respectively, then (a) b+c=4a (b) b+c=2a (c) the locus of point A is an ellipse (d) the locus of point A is a pair of straight lines

In a triangle ABC, if sin A sin(B-C)=sinC sin(A-B) , then prove that cos 2A,cos2B and cos 2C are in AP.

If the angles A,B,C of a triangle are in A.P. and sides a,b,c, are in G.P., then prove that a^2, b^2,c^2 are in A.P.

In any triangle A B C , prove that: (1+cos(A-B)cos C)/(1+cos(A-C)cos B)=(a^2+b^2)/(a^2+c^2)

If Delta ABC is right triangle and if angleA = (pi)/(2) , then prove that cos B - cos C = -1 + 2 sqrt(2) cos"" (B)/(2) sin"" (C )/(2) .