What is the value of x?

We know that cos(A)=sin(90-A)

 

We also know that if sin(A)=sin(B) then B=A+360K or B=180-A+360K (think about it)

 

 

sin(x+37)=cos(2x+8)=sin(90-8-2x)=sin(82-2x)

 

FIRST OPTION:

 

x+37=82-2x+360K   / add 2x, and subtract 37

 

3x=45+360K    / divide by 3

 

x=15+120K

 

 

SECOND OPTION:

 

x+37=180-(82-2x)+360K=98+2x+360K   / subtract (37+2x)

 

-x=61+360K   / divide by -1

 

x=-360K-61