Question

Решите пример из тригонометрии
7вар.4 пример

Answer 1

$(Sin^{4}(\frac{3\pi }{2}-\frac{\pi }{24})-Sin^{4}(\pi+\frac{\pi }{24}))*Sin(2\pi+\frac{\pi }{12})*Sin(4\pi+\frac{\pi }{6})=(Cos^{4}\frac{\pi }{24}-Sin^{4}\frac{\pi }{24})*Sin\frac{\pi }{12}*Sin\frac{\pi }{6}=(Cos^{2}\frac{\pi }{24}+Sin^{2}\frac{\pi }{24})(Cos^{2}\frac{\pi }{24}-Sin^{2}\frac{\pi }{24})*Sin\frac{\pi }{12}*\frac{1}{2}=$$=\frac{1}{2} Cos\frac{\pi }{12}Sin\frac{\pi }{12}=\frac{1}{4}*2Cos\frac{\pi }{12}Sin\frac{\pi }{12}=\frac{1}{4}Sin\frac{\pi }{6}=\frac{1}{4} *\frac{1}{2}=\frac{1}{8}=0,125$