If a, b and A are given in a triangle and `c_(1), c_(2)` are possible values of the third side, then prove that `c_(1)^(2) + c_(2)^(2) - 2c_(1) c_(2) cos 2A = 4a^(2) cos^(2)A`

If a, b, A be given in a triangle and c_1 and c_2 be two possible value of the third side such that c_1^2+c_1c_2+c_2^2=a^2, then a is equal to

In Delta ABC, a, b and A are given and c_(1), c_(2) are two values of the third side c. Prove that the sum of the area of two triangles with sides a, b, c_(1) and a, b c_(2) " is " (1)/(2) b^(2) sin 2A

In a Delta ABC, a,b,A are given and c_(1), c_(2) are two values of the third side c. The sum of the areas two triangles with sides a,b, c_(1) and a,b,c_(2) is

In the ambiguous case, if a, b and A are given and c_1, c_2 are the two values of the third (c_1-c_2)^2 + (c_1+c_2)^2 tan^2 A is equal to

In a delta ABC, a,c, A are given and b_(1) , b_(2) are two values of third side b such that b_(2)=2b_(1). Then, the value of sin A.

When any two sides and one of the opposite acute angle are given, under certain additional conditions two triangles are possible. The case when two triangles are possible is called the ambiguous case. In fact when any two sides and the angle opposite to one of them are given either no triangle is posible or only one triangle is possible or two triangles are possible. In the ambiguous case, let a,b and angle A are given and c_(1), c_(2) are two values of the third side c. On the basis of above information, answer the following questions The value of c_(1)^(2) -2c_(1) c_(2) cos 2A +c_(2)^(2) is

Prove that (cos^(2)A-sin^(2)B)+1-cos^(2)C

Prove that a(b^(2) + c^(2)) cos A + b(c^(2) + a^(2)) cos B + c(a^(2) + b^(2)) cos C = 3abc

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

If A+B+C=180^@ , then prove that cos^2 A + cos^2 B +cos^2 C=1-2cosA cosB cosC .