Question

Points D, E are taken on the side BC of a triangle ABC such that BD = DE = EC. If ∠BAD = x, ∠DAE = y, ∠EAC = z, then the value of sin(x + y)sin(y + z)/sin x sin z  is equal to

(A)  4

(B)  1 

(C)  2 

(D)  None of these

Answer 1

Correct option  (A) 4

See Fig. From ∆ADC

sin(y + z)/DC = SinC/AD   .....(i)

From ∆ABD  sinx/BD = sinB/AD   .....(2)

and from ∆AEC, sinz/EC = sinC/AE    .....(3)

Also, from ∆ABE, sin(x + y/BE) = sinB/AE  .....(4)

From Eqs. (1), (2), (3) and (4), we get