Question

Решите пример из тригонометрии
7вар.4 пример

Answer 1

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