If in triangle `A B ,cosAcosB+sinAsinBsinC=1.` Show that `a : b : c=1:1:sqrt(2)`

Prove that in triangle A B C ,cos^2A+cos^2B-cos^2C=1-2sinAsinBcosCdot

Let a,b,c be the sides of a triangle ABC, a=2c,cos(A-C)+cos B=1. then the value of C is

In any triangle A B C ,sin^2A-sin^2B+sin^2C is always equal to (A) 2sinAsinBcosC (B) 2sinAcosBsinC (C) 2sinAcosBcosC (D) 2sinAsinBsinC

If Delta is the area of a triangle with side lengths a, b, c, then show that as Delta leq 1/4 sqrt((a + b + c) abc) Also, show that the equality occurs in the above inequality if and only if a = b = c .

In DeltaABC , if sin A + sin B + sin C= 1 + sqrt2 and cos A+cos B+cosC =sqrt2 then the triangle is

If in triangle ABC, a, c and angle A are given and c sin A lt a lt c , then ( b_(1) and b_(2) are values of b)

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))

in a triangle ABC , ( cos A)/(a) = (cos B )/( b) = ( cos C )/( c ) if a=(1 )/( sqrt(6)) then the area of the triangle ( in square units ) is

Show that the line joining the incenter to the circumcenter of triangle A B C is inclined to the side B C at an angle tan^(-1)((cosB+cosC-1)/(sinC-sinB))

A(z_1),B(z_2),C(z_3) are the vertices of the triangle A B C (in clockwise). If /_A B C=pi//4 and A B=sqrt(2)(B C) , then prove that z_2=z_3+i(z_1-z_3)dot