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Agustín Valverde Ramos edited Soluci_n_begin_aligned_cos__.tex
over 8 years ago
Commit id: 48327d716bbca91b9a6fbc14dd0ed6b27f0a9609
deletions | additions
diff --git a/Soluci_n_begin_aligned_cos__.tex b/Soluci_n_begin_aligned_cos__.tex
index 8e31cbb..139597f 100644
--- a/Soluci_n_begin_aligned_cos__.tex
+++ b/Soluci_n_begin_aligned_cos__.tex
...
Solución:
\[
\begin{aligned}
\cos(5\theta) & = \mathrm{Re}((\cos \theta+\mathrm{i}\sin\theta)^5) = \\
& = \mathrm{Re}(\cos^5 \theta+5\mathrm{i}\cos^4\theta\sin\theta
−10\cos^3 \theta\sin^2 \theta
−10\mathrm{i}\cos^2\theta\sin^3\theta
+5\cos \theta\sin^4 \theta
+\mathrm{i}\sin^5\theta) = \\
& = \cos^5 \theta−10\cos^3 \theta\sin^2 \theta+5\cos \theta\sin^4 \theta = \\
& = \cos^5 \theta−10\cos^3 \theta(1-\cos^2\theta)+5\cos \theta(1-\cos^2\theta)^2 = \\
& = \cos^5 \theta−10\cos^3 \theta+10\cos^5\theta+5\cos \theta(1-2\cos^2\theta+\cos^4\theta) = \\
& = \cos^5 \theta−10\cos^3 \theta+10\cos^5\theta+5\cos \theta-10\cos^3\theta+5\cos^5\theta = \\
& = 16\cos^5 \theta−20\cos^3 \theta+5\cos \theta
\end{aligned}
\]
