Not sure where this belonged in the forum, but hopefully I got close.
I need to find values for c and x, that are both real and positive that satisfy this equation. Im pretty sure that Euler's formula will be of use, I cant figure out what the first step would be. Thanks.
cos(4t-1) - 2sin(4t+2) = c cos(4t+x)
I tried splitting these up with trig identities before and got:
cos(1)cos(4t) + sin(1)sin(4t) - 2cos(4t)sin(2) + 2cos(2)sin(4t)
Next, I factored out the constants. getting:
[cos(1)-2sin(2)]cos(4t) + [sin(1)+2cos(2)]sin(4t).
Now I just gotta find a way to combine these and just get a cosine term on the left side so that it will match the right.
Your original idea to use Euler's formula seems to me pretty good!... remember that from the Euler's formula...
(1)
... You can derive the identities...
(2)
(3)
What I suggest to You is to write all sin and cos in Your equation in 'exponential form' and then to set, for example, ...
Kind regards