Question

Point D,E are taken on the side BC of an acute angled triangle ABC,, such that BD = DE = EC. If angle BAD = x, angle DAE = y and angle EAC = z then the value of (sin(x+y) sin (y+z))/(sinx sin z) is ______

Answer 1

Step-by-step explanation:

We have, BD=DE=EC=31a

ln△ABE,32asin(x+y)=AEsinB     ...(1)

ln△ADC,32asin(y+z)=ADsinC     ...(2)

ln△ABD,31asinx=ADsinB      ...(3) 

ln△AFC,31asinz=AEsinC     ...(4)

From (1), (2), (3), and (4), we have 

sinxsinzsin(x+y)sin(y+z)=4.

Answer 2

We have, BD=DE=EC=31a

ln△ABE,32asin(x+y)=AEsinB     ...(1)

ln△ADC,32asin(y+z)=ADsinC     ...(2)

ln△ABD,31asinx=ADsinB      ...(3)  

ln△AFC,31asinz=AEsinC     ...(4)

From (1), (2), (3), and (4), we have  

sinxsinzsin(x+y)sin(y+z)=4.