Can I Add Sine and Cosine Functions with a Non-Factorable Scalar?

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To add sine and cosine functions with non-factorable scalars, expand the cosine term using the angle addition formula. For example, in the expression 5*cos(wt) + 6*cos(wt + π/4), first expand cos(wt + π/4) into its components. After expansion, group like terms to simplify the expression. The result can be expressed in the form R*cos(wt ± A) or R*sin(wt ± A). This method allows for the combination of the functions despite the presence of scalars.
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Homework Statement



Hi guys,

I don't know if this should go here because it is an excerpt from a higher level problem. The part where I get stuck is when I try to add the cosine functions.

Is there any way to add sine and cosine functions that have a scalar in front that cannot be factored out? For example:

5*cos(wt) + 6*cos(wt + pi/4)

If there weren't any numbers in front of the functions then I could use the trig identity. What can I do with the numbers there? Thanks
 
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5cos(wt) + 6*cos(wt + π/4)


expand out cos(wt+π/4) then group the like terms. Then you can either put in the form Rcos(wt±A) or Rsin(wt±A)
 
cos(A+ B)= cops(A)cos(B)- sin(A)sin(B).
 

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