Question

Тригонометрия помогите с 9-ым заданием

Answer 1

$Sin(frac{5pi }{2}+4alpha)=Sin(2pi +(frac{pi }{2}+4alpha))=Sin(frac{pi }2}+4alpha)=Cos4alpha=8Cos^{4}alpha -8Cos^{2}alpha+1\\1+tg^{2}alpha=frac{1}{Cos^{2}alpha }\\Cos^{2}alpha=frac{1}{1+tg^{2}alpha}=frac{1}{1+(sqrt{7})^{2}}=frac{1}{1+7}=frac{1}{8}\\8Cos^{4}alpha-8Cos^{2}alpha+1=8*(frac{1}{8})^{2}-8*frac{1}{8}+1=frac{1}{8}-1+1=frac{1}{8}=0,125$