Question

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Answer 1

$1)Sin\frac{17\pi }{24}Cos\frac{9\pi }{24}-Cos\frac{17\pi }{24}Sin\frac{9\pi }{24}=Sin(\frac{17\pi }{24}-\frac{9\pi }{24})=Sin\frac{8\pi }{24}=Sin\frac{\pi }{3}=\frac{\sqrt{3}}{2}$

$2)Cos\frac{17\pi }{24}Cos\frac{5\pi }{24}+Sin\frac{17\pi }{24}Sin\frac{5\pi}{24}=Cos(\frac{17\pi }{24}-\frac{5\pi }{24})=Cos\frac{12\pi }{24} =Cos\frac{\pi}{2}=0$

$3)Sin112^{o}Cos22^{o}-Sin22^{o}Cos112^{o}=Sin(112^{0}-22^{o})=Sin90^{0}=1$

$4)\frac{Sin72^{o}Cos12^{0}-Sin12^{o}Cos72^{o}}{Cos12^{0}Cos18^{0}-Sin12^{0}Sin18^{0}}=\frac{Sin(72^{o}-12^{o} )}{Cos(12^{o}+18^{0}}=\frac{Sin60^{o}}{Cos30^{o}}=\frac{\sqrt{3}}{2}:\frac{\sqrt{3}}{2}=1$

$5)\frac{tg29^{0}+tg16^{0}}{1-tg29^{o}tg16^{0}}=tg(29^{o}+16^{o})=tg45^{o}=1$

$6)Cos^{2}\frac{5\pi }{12}-Sin^{2}\frac{5\pi}{12}=Cos(2*\frac{5\pi }{12})=Cos\frac{5\pi }{6}=Cos(\pi-\frac{\pi }{6})=-Cos\frac{\pi }{6}=-\frac{\sqrt{3}}{2}$

$7)2Sin\frac{\pi }{8}Cos\frac{\pi }{8}=Sin(2*\frac{\pi }{8})=Sin\frac{\pi }{4}=\frac{\sqrt{2} }{2}$

$8)\frac{2tg75^{o}}{1-tg^{2}5^{o}}=tg(2*75^{o})=tg150^{o}=tg(180^{o}-30^{o})=-tg30^{o}=-\frac{\sqrt{3}}{3}$