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

If in a /_\ ABC, cosA.cosB+sinA.sinB.sinC =1,then (A) A=B (B) C=pi/2 (C) AC=BC (D) AB=sqrt(2) AC

The angles of a triangle ABC are in A.P. and it is being given that b:c= sqrt(3) : sqrt(2) , find angleA .

If a ,b ,c are the sides of a triangle such that a : b : c=1:sqrt(3):2, then ratio A : B : C is equal to a.3:2:1 b. 3:1:2 c. 1:2:3 d. 1:3:2

If a ,b ,c are the sides of a triangle such that a : b : c=1:sqrt(3):2, then ratio A : B : C is equal to 3:2:1 b. 3:1:2 c. 1:2:3 d. 1:3:2

D is a point on the side BC of a triangle ABC such that /_A D C=/_B A C . Show that C A^2=C B.C D .

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

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

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 .

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 .

Problem on sine rule Type:-1(i) In a DeltaABC ; If a=2;b=3 and sinA=2/3 ;find /_B (ii) In a DeltaABC ; the angle of a triangle are in AP ; It is being given that b:c=sqrt3:sqrt2