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Counter-Strike: Source (2004)

Duration: 5:15

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Using trigonometric relation \( \sin A \sin B \)
\( =1 / 2[\cos (A-B)]-\cos (A+B) \), we can write
\( c_{m}(t)=A_{c} \sin \omega_{c} t+\mu A_{c} \sin \omega_{m} t \sin \omega_{c} t \) as follows
(a) \( c_{m}(t)=A_{c} \sin \omega_{m} t+\frac{\mu A_{c}}{2} \cos \left(\omega_{c}-\omega_{m}\right) t \)
\[
-\frac{\mu A_{c}}{2} \cos \left(\omega_{c}+\omega_{m}\right) t
\]
(b) \( c_{m}(t)=A_{c} \sin \omega_{c} t+\frac{\mu A_{m}}{2} \cos \left(\omega_{c}-\omega_{m}\right) t \)
\[
-\frac{\mu A_{m}}{2} \cos \left(\omega_{c}+\omega_{m}\right) t
\]
- (c) \( c_{m}(t)=A_{c} \sin \omega_{c} t+\frac{\mu A_{c}}{2} \cos \left(\omega_{c}-\omega_{m}\right) t \)
\[
-\frac{\mu A_{c}}{2} \cos \left(\omega_{c}+\omega_{m}\right) t
\]
- (d) \( c_{m}(t)=A_{c} \sin \omega_{c} t+\frac{\mu A_{c}}{2} \cos \left(\omega_{c}+\omega_{m}\right) t \)
\[
-\frac{\mu A_{c}}{2}\left(\omega_{c}-\omega_{m}\right) t
\]
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