If f,g,h are internal bisectoirs of the angles of a triangle ABC, show that `1/f cos, A/2+ 1/g cos, B/2+1/h cos, C/2= 1/a+1/b+1/c`

In any Delta ABC, show that cos A+ cos B+ cos C = (1+ (r )/(R )).

If cos 3A +cos 3B+cos 3C=1 then one of the angles of the triangle ABC is

In triangle ABC , prove that (1) a=b cos C+c cos B (2) b=a cos C+c cos A .

If x,y,z be the lengths of the internal bisectors of the angles of a triangle 1,m,n be the lengths of these bisectors produced to meet the circumcircle,then show that x^(-1)cos((A)/(2))+y^(-1)cos((B)/(2))+z^(-1)cos((C)/(2))=a^(-1)+b^(-1)+c^(-1)

If A,B,C are interior angles of /_ABC, show that : : cos ec^(2)((B+C)/(2))-tan^(2)((A)/(2))=1

If A , Ba n dC are the angels of a triangle, show that |-1+cos B cos C+cos B cos B cos C+cos A-1+cos A cos A-1+cos B-1+cos A-1|=0

If A,B,C are the angles of triangle ABC, then the minimum value of |{:(-2,cos C , cos B),(cos C , -1, cos A ) , (cos B , cos A , -1):}| is equal to :

If A,B,C are the angles of triangle ABC, then the minimum value of |{:(-2,cos C , cos B),(cos C , -1, cos A ) , (cos B , cos A , -1):}| is equal to :

If A,B,C are the angles of a triangle then prove that cos A+cos B-cos C=-1+4cos((A)/(2))cos((B)/(2))sin((C)/(2))

Statement-1: In a triangle ABC, if sin^(2)A + sin^(2)B + sin^(2)C = 2 , then one of the angles must be 90 °. Statement-2: In any triangle ABC cos 2A + cos 2B + cos 2C = -1 - 4 cos A cos B cos C