Your problem should have been stated:
Given
,
Determine the values of a and b.

We look up the formulas for sin(5A), cos(5A), and cos(4A)



 









We change the sines in the first two terms to cosines.  To change the first
term:

 

To change the second term



Substituting:



Simplifying:



This will be an identity if and only if the numerical coefficients on the left
are equal to the literal coefficients of corresponding like terms on the right.

 

Either of the first two equations give b=4, substituting in the third
6=a+4 or a=2.

Answer: a=2, b=4

Edwin