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guys I am struggling with the expansion from the second last line to the last for this problem. Any suggestions with examples would be highly appreciated. Thanks a lotenter image description here

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You use $\cos(A+B)=\cos A\cos B-\sin A\sin B,\cos(A-B)=\cos A\cos B+\sin A\sin B$. So $\cos(A-B)-\cos(A+B)=2\sin A\sin B$.

Takng $A=5\pi10^7t-0.2\pi,B=0.2\pi$ we get $\cos(5\pi10^7t-0.4\pi)-\cos(5\pi10^7t)=2\sin(5\pi10^7t-0.2\pi)\sin(0.2\pi)$

So we have the desired expression provided $3\sin(0.2\pi)=1.76$.

That is indeed true - either use a calculator or note that $\sin\frac{\pi}{5}=\sqrt{\frac{5-\sqrt5}{8}}$

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  • $\begingroup$ THANKS A LOT!REALLY HELPFUL $\endgroup$ – Silent pain Jun 20 '16 at 21:09
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$$\cos(C)-\cos(D)=2\sin({C+D\over 2})\sin({D-C\over 2})$$

Take $C=5\pi 10^7t-0.4\pi$ and $D=5\pi10^7t$

Now use a calculator

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    $\begingroup$ @Silentpain As a member of the community, do upvote answers (and questions)if you like them. $\endgroup$ – Qwerty Jun 21 '16 at 4:20

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