Complex Fourier Series

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Sonia1234

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Hello guys,

I have a small confusion in the attached question. First I converted the sin^2 using formula to cosine. Then I used scaling property which states that x(t) becomes (1/a) X(w/a). Okay for simplicity, w means omega. I currently have x(t)=cos(wt) + ((1/2)-(1/2)cos(2wt)) and I really don't know how would I find X(w) and apply the scaling property over it. Any help would be whole heartedly appreciated.
Waiting for your replies.
 

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\[\cos {\omega}t + \sin^2{\omega}t = \cos{\omega}t + \frac{1}{2} - \displaystyle\frac{\cos{2\omega}t}{2}\]

and

\[\cos{\omega}t = \displaystyle\frac{e^{{j\omega}t}+e^{-{j\omega}t}}{2}\]

Then ....
 

Look I have alrady solved this thing using Euler's but the point is now I want to solve it using the property. The main thing is "I need to use the property". And how would I do that? That's why I'm here!
 

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