Why this equation has no solution in R ?

[Vali]

I need to find the solution of \(\displaystyle \sin(x)\sin(2x)\sin(3x)...\sin(100x)=1\)

This mean every member should be 1 or -1, right?
I draw sin(2x) and sin(3x) graph and they take value 1 for different x.What does it mean ?It's not clear for me why this equation has no solutions in R.

 

[lev888]

For which values of x sin(x) is 1?

 

[Vali]

pi/2 +2kpi

 

[lev888]

pi/2 +2kpi

Now look at sin(2x) when x is pi/2 +2kpi.

 

[Vali]

I get sin(2x)=sin(pi+4kpi)

 

[lev888]

I get sin(2x)=sin(pi+4kpi)

Which is?

 

[Vali]

0

 

[lev888]

0

Yep.

 

[Steven G]

So can you know see why the product can never equal 1?

 

[Vali]

Yes,thanks!