`|[-1,cos C,cos B],[cos C,-1,cos A],[cos B,cos A,-1]|=0`

If A, B and C denote the angles of a triangle, then Delta = |(-1,cos C,cos B),(cos C,-1,cos A),(cos B,cos A,-2)| is independent of

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

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 , 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

In a Delta A B C , prove the following : \ a(cos B+cos C-1)+b(cos C+cos A-1)+c(cos A+cos B-1)=0 .

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

If three angles A, B, C are such that cos A+ cos B + cos C = 0 and if lambda cos A cos B cos C = cos 3A + cos 3B + cos 3C , then value of lambda is :

Prove that : (sin 2A+sin 2B + sin 2C)/(cos A + cos B + cos C-1) = 8 cos(A/2) cos( B/2) cos( C/2)

In any triangle A B C , prove that following: \ a\ (cosB cos C+cos A)=b(cos C\ cos A+cos B)=c(cos A\ cos B+cos C)dot

If |{:(1,cos alpha, cos beta),(cos alpha, 1 , cos gamma ),(cos beta, cos gamma , 1):}|=|{:(0,cos alpha, cos beta),(cos alpha , 0 , cos gamma),(cos beta, cos gamma, 0):}| then the value of cos^2 alpha + cos^2 beta + cos^2 gamma is : (a) 1 (b) 1/2 (c) 3/8 (d) 9/4