how to slove this .. !! please cos(x)cos(2x)cos(4x)cos(8x)= sin(16x)/sin(x)

Question

cos(x)cos(2x)cos(4x)cos(8x)= sin(16x)/sin(x)

PLEASE URGENT GUYS!

Answer 1

Use the double angle formula:  sin(2θ)=2sinθcosθ

 

sin(16x) = sin[2(8x)] 

 

               = 2sin(8x)cos(8x)

 

               = 2sin[2(4x)]cos(8x)

 

               = 2(2)sin(4x)cos(4x)cos(8x)

 

               = 4sin[2(2x)]cos(4x)cos(8x)

 

               = 4(2)sin(2x)cos(2x)cos(4x)cos(8x)

 

               = 8(2)sinxcosxcos(2x)cos(4x)cos(8x)

 

So, sin(16x)/(16sinx)=cosxcos(2x)cos(4x)cos(8x)

 

It looks like the denominator of the right hand side of the given equation should be 16sinx, not sinx.  

Answer 2

sin(16x) = 2sin(8x)cos(8x)=4sin(4x)cos(4x)cos(8x)

             = 8sin(2x)cos(2x)cos(4x)cos(8x)

             = 16sin(x)cos(x)cos(2x)cos(4x)cos(8x)

 

sin(16x)/sin(x) should be 16cos(x)cos(2x)cos(4x)cos(8x)

 

Can you check with your problem? we are a factor of 16 off.