Mathematics, 27.07.2019 03:10 meep26wesley
use the information above (2nd picture) and the trigonometric identities to prove that (1st picture)
Answers: 1
![\bf \textit{Sum and Difference Identities} \\\\ sin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta) \\\\ sin(\alpha - \beta)=sin(\alpha)cos(\beta)- cos(\alpha)sin(\beta) \\\\[-0.35em] \rule{34em}{0.25pt}](/tpl/images/0137/2981/7e85f.png)
![\bf c_2sin(\omega t)+c_1cos(\omega t)~~ \begin{cases} c_2=Acos(\theta )\\ c_1=Asin(\theta ) \end{cases} \\\\\\ Acos(\theta )sin(\omega t)+Asin(\theta )cos(\omega t)\implies Asin(\omega t)cos(\theta )+Acos(\omega t)sin(\theta ) \\\\\\ \stackrel{\textit{common factor}}{A[sin(\omega t)cos(\theta )+cos(\omega t)sin(\theta )]}\implies A[sin(\omega t + \theta) ]\implies Asin(\omega t + \theta)](/tpl/images/0137/2981/9ce1f.png)
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use the information above (2nd picture) and the trigonometric identities to prove that (1st picture)...
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