Linear Combination of Cosine Function

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How would I express cos(wt+1) as a linear combination of cos(wt) and sin(wt)?
 
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Basic formula: cos(x+y)=cos(x)cos(y)-sin(x)sin(y). You should be able to take it from there.
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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