Toán Lớp 9: cos^2 20° + cos^2 40° + cos^2 50° + cos^2 70°
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Toán Lớp 9: cos^2 20° + cos^2 40° + cos^2 50° + cos^2 70°
Comments ( 2 )
\text{Ta có:}\ \cos(90^\circ -\alpha) = \sin\alpha\\
\text{Do đó:}\\
\cos20^\circ = \sin70^\circ\\
\cos40^\circ = \sin50^\circ\\
\text{Ta được:}\\
\quad \cos^220^\circ + \cos^240^\circ + \cos^250^\circ + \cos^270^\circ\\
= \sin^270^\circ + \sin^250^\circ+ \cos^250^\circ + \cos^270^\circ\\
= (\sin^270^\circ + \cos^270^\circ) + (\sin^250^\circ + \cos^250^\circ)\\
= 1 + 1\\
= 2
\end{array}\)