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\(\begin{array}{l}
a)\cos \frac{{22\pi }}{3}\\
b)\sin \frac{{23\pi }}{4}\\
c)\sin \frac{{25\pi }}{3} - \tan \frac{{10\pi }}{3}\\
d){\cos ^2}\frac{\pi }{8} - {\sin ^2}\frac{\pi }{8}
\end{array}\)
\(\begin{array}{l}
a)\cos \frac{{22\pi }}{3} = \cos \left( {\frac{{21\pi + \pi }}{3}} \right) = \cos \left( {\frac{\pi }{3} + 7\pi } \right) = \cos \left( {\frac{\pi }{3} + \pi + 6\pi } \right)\\
= \cos \left( {\frac{\pi }{3} + \pi + 3.2\pi } \right)\left( {k = 3} \right)\\
= \cos \left( {\frac{\pi }{3} + \pi } \right) = - \cos \frac{\pi }{3} = - \frac{1}{2}\\
b)\sin \frac{{23\pi }}{4} = \sin \left( {\frac{{24\pi - \pi }}{4}} \right) = \sin \left( {6\pi - \frac{\pi }{4}} \right) = \sin \left( { - \frac{\pi }{4}} \right) = - \sin \frac{\pi }{4} = - \frac{{\sqrt 2 }}{2}
\end{array}\)
\(\begin{array}{l}
c)\sin \frac{{25\pi }}{3} - \tan \frac{{10\pi }}{3} = \sin \frac{{24\pi + 1\pi }}{3} - \tan \left( {\frac{{9\pi + \pi }}{3}} \right)\\
= \sin \left( {8\pi + \frac{\pi }{3}} \right) - \tan \left( {3\pi + \frac{\pi }{3}} \right)\\
= \sin \frac{\pi }{3} - \tan \frac{\pi }{3} = \frac{{\sqrt 3 }}{2} - \sqrt 3 = - \frac{{\sqrt 3 }}{2}
\end{array}\)
Đặt \(a = \frac{\pi }{8} \Rightarrow 2a = \frac{\pi }{4}\)
\(\begin{array}{l}
{\cos ^2}\frac{\pi }{8} = \frac{{1 + \cos \frac{\pi }{4}}}{2} = \frac{{2 + \sqrt 2 }}{4};{\sin ^2}\frac{\pi }{8} = \frac{{1 - \cos \frac{\pi }{4}}}{2} = \frac{{2 - \sqrt 2 }}{4}\\
\Rightarrow {\cos ^2}\frac{\pi }{8} - {\sin ^2}\frac{\pi }{8} = \frac{{\sqrt 2 }}{2}
\end{array}\)
-- Mod Toán 10