[tex]a) ...=\cos(98-53)=\cos45=\frac{\sqrt2}{2}\\b) ...=\sin(56-26)=\sin30=0,5\\c) ...=\sin(\frac{8\pi}{7}+\frac{6\pi}{7})=\sin2\pi =0\\d) ...=\cos(3\alpha +2\alpha )=\cos 5\alpha \\e) \\...=\cos\alpha \cos\frac{\pi}{4}-\sin\alpha \sin\frac{\pi}{4}[/tex]
При данных в условии ограничениях на [tex]\alpha[/tex] [tex]\sin\alpha < 0[/tex]
[tex]\sin\alpha =-\sqrt{1-\cos^{2}\alpha } =-\frac{4}{5}[/tex]
[tex]\cos\alpha \cos\frac{\pi}{4}-\sin\alpha \sin\frac{\pi}{4}=-\frac{3}{5}\frac{\sqrt{2} }{2} - (-\frac{4}{5} \frac{\sqrt2}{2})=\frac{\sqrt2}{10}[/tex]
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[tex]a) ...=\cos(98-53)=\cos45=\frac{\sqrt2}{2}\\b) ...=\sin(56-26)=\sin30=0,5\\c) ...=\sin(\frac{8\pi}{7}+\frac{6\pi}{7})=\sin2\pi =0\\d) ...=\cos(3\alpha +2\alpha )=\cos 5\alpha \\e) \\...=\cos\alpha \cos\frac{\pi}{4}-\sin\alpha \sin\frac{\pi}{4}[/tex]
При данных в условии ограничениях на [tex]\alpha[/tex] [tex]\sin\alpha < 0[/tex]
[tex]\sin\alpha =-\sqrt{1-\cos^{2}\alpha } =-\frac{4}{5}[/tex]
[tex]\cos\alpha \cos\frac{\pi}{4}-\sin\alpha \sin\frac{\pi}{4}=-\frac{3}{5}\frac{\sqrt{2} }{2} - (-\frac{4}{5} \frac{\sqrt2}{2})=\frac{\sqrt2}{10}[/tex]