SOLUTION: sin(4x)cos(3x)+cos(4x)sin(3x)=0.51 solve by finding exact values for two fundamental solutions.

sin(4x)cos(3x)+cos(4x)sin(3x)=0.51

Use the identity

  

Substitute , :

  

or

  

  

The right side equals to 0.51.  

Take inverse sines of both sides:

  sin-1(0.51) + 

also

  ( - sin-1(0.51) + )

  -sin-1(0.51) + )
Therefore, solving for x in each

  sin-1(0.51) + 

also

  sin-1(0.51) + )

To get the two fundamental solutions let n=0 in each:


  sin-1(0.51)

and


  sin-1(0.51) + 

Edwin