George Bray

2022-06-19

Find the value of $\mathrm{sin}\frac{\pi }{10}-\mathrm{sin}\frac{3\pi }{10}$

Schetterai

$\mathrm{sin}\frac{\pi }{10}-\mathrm{sin}\frac{3\pi }{10}=\mathrm{cos}{72}^{\circ }+\mathrm{cos}{144}^{\circ }=$
$=\frac{2\mathrm{sin}{36}^{\circ }\mathrm{cos}{72}^{\circ }+2\mathrm{sin}{36}^{\circ }\mathrm{cos}{144}^{\circ }}{2\mathrm{sin}{36}^{\circ }}=$
$=\frac{\mathrm{sin}{108}^{\circ }-\mathrm{sin}{36}^{\circ }+\mathrm{sin}{180}^{\circ }-\mathrm{sin}{108}^{\circ }}{2\mathrm{sin}{36}^{\circ }}=-\frac{1}{2}.$
done!

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