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

If A,B,C are the angles of a given triangle ABC . If cosA.cosB.cosC= (sqrt3-1)/8 and sinA.sinB.sinC= (3+sqrt3)/8 The value of tanA+tanB+tanC is (A) (3+sqrt(3)/(sqrt(3)-1)) (B) (sqrt(3)+4/(sqrt(3)-1)) (C) (6-sqrt(3)/(sqrt(3)-1)) (D) (sqrt(3)+sqrt(2)/(sqrt(3)-1))

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

In a triangle A B C , a line X Y is drawn parallel to B C meeting A B in X and A C in Y . The area of the triangle A X Y is half of the area of the triangle A B C . X Y divides A B in the ratio of 1 :sqrt(2) (b) sqrt(2) :(sqrt(2)-1) (c) 1 :(sqrt(2)-1) (d) sqrt(2) :sqrt(3)

In Delta ABC, if sin A+sin B+sin B+sin C=1+sqrt(2) and cos A+cos B+cos C=sqrt(2) then the triangle is

In a !ABC , sin A + sin B + sin C = 1+ sqrt2 and ,cos A +cos B +cos C = sqrt2 if ,the triangle is

If in a triangle ABC, |{:(1, sin A ,sin^(2)A),(1,sin B , sin^(2)B),(1, sin C, sin^(2)C):}|= 0 then the triangle is

If Delta is the area of a triangle with side lengths a,b,c, then show that as Delta<=(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 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.3:2:1b.3:1:2 c.1:2:3 d.1:3:2

If in a triangle A B C ,(1+cosA)/a+(1+cosB)/b+(1_(cosC))/c =(k^2(1+cosA)(1+cosB)(1+cosC)/(a b c) , then k is equal to 1/(2sqrt(2)R) (b) 2R (c) 1/R (d) none of these