In a triangle `DeltaXYZ`, let a,b and c be the lengths of the sides opposite to the angles X,Y and Z, respectively. If `2(a^2-b^2)=c^2` and `lambda=sin(X-Y)/(sinZ,`then possible values of n for which `cos(npilambda)=0` is (are)

In a triangle DeltaXYZ, let a, b, and c be the length of the sides opposites to the angles X,Y and Z, respectively.If 1+cos2X-2cos2Y=2sinXsinY , then possible value(s) of a/b is (are)

In a triangle XYZ, let x, y, z be the lengths of sides opposite to the angles X, Y, Z, respectively, and 2s = x + y + z. If (s-x)/4=(s-y)/3=(s-z)/2 and area of incircle of the triangle XYZ is (8pi)/3 . then the area of triangle XYZ is _

In a DeltaABC, a,b,c are the sides of the triangle opposite to the angles A,B,C respectively. Then the value of a^3sin(B-C)+b^3 sin(C-A)+c^3 sin(A-B) is equal to

Let PQR be a triangle of area Delta with a=2,b=7/2 and c=5/2 , where a,b and c are the lengths of the sides of the triangle opposite to the angles at P,Q and R respectively. Then ((2sinP-sin2P)/ (2sinP+sin2P)) equals

Let ABC is be a fixed triangle and P be veriable point in the plane of triangle ABC. Suppose a,b,c are lengths of sides BC,CA,AB opposite to angles A,B,C, respectively. If a(PA)^(2) +b(PB)^(2)+c(PC)^(2) is minimum, then point P with respect to DeltaABC is

Consider a triangle A B C and let a , ba n dc denote the lengths of the sides opposite to vertices A , B ,a n dC , respectively. Suppose a=6,b=10 , and the area of triangle is 15sqrt(3)dot If /_A C B is obtuse and if r denotes the radius of the incircle of the triangle, then the value of r^2 is

Let A B C be a triangle such that /_A C B=pi/6 and let a , b and c denote the lengths of the side opposite to A , B ,and C respectively. The value(s) of x for which a=x^2+x+1,b=x^2-1,\and\ c=2x+1 is(are) -(2+sqrt(3)) (b) 1+sqrt(3) (c) 2+sqrt(3) (d) 4sqrt(3)

Let a, b and c be the three sides of a triangle, then prove that the equation b^2x^2+(b^2+c^2-a^2)x+c^2=0 has imaginary roots.

Let alt=blt=c be the lengths of the sides of a triangle. If a^2+b^2 < c^2, then prove that triangle is obtuse angled .

If the angle A ,Ba n dC of a triangle are in an arithmetic propression and if a , ba n dc denote the lengths of the sides opposite to A ,Ba n dC respectively, then the value of the expression a/csin2C+c/asin2A is (a) 1/2 (b) (sqrt(3))/2 (c) 1 (d) sqrt(3)