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# If sinx+siny=root3(cosy-cosx)Prove that sin3x+sin3y=0.

Sunil Raikwar
7 years ago
sinx+siny = root3 ( cosx-cosy)
2sin(x+y/2)cos(x-y/2) = root3 {2sin(x+y/2)sin(y-x/2)}
sin(x+y/2)[cos(x-y/2)-root3. sin(y-x/2)]=0
sin(x+y/2)= 0
x= -y.......................1
or cos(x-y/2)=root3. sin(y-x/2)
tan(x-y/2)=- 1/root3
then x-y/2 = - pie/6
x = - pie/3 +y...........2
putting the value of x from 1 & 2 in sin3x+sin3y we get the required answer.

Sumit Majumdar IIT Delhi
7 years ago
Dear student,
According to the given relation, we would have:
If we multiply both sides by a factor of 4, we get:
This on simplifying gives us:
If the right hand side can be simplified to zero, we get the answer.
Regards
Sumit