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) of these
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
