Question

Тригонометрия помогите с 9-ым заданием

Answer 1

$Sin(\frac{5\pi }{2}+4\alpha)=Sin(2\pi +(\frac{\pi }{2}+4\alpha))=Sin(\frac{\pi }2}+4\alpha)=Cos4\alpha=8Cos^{4}\alpha -8Cos^{2}\alpha+1\\\\1+tg^{2}\alpha=\frac{1}{Cos^{2}\alpha }\\\\Cos^{2}\alpha=\frac{1}{1+tg^{2}\alpha}=\frac{1}{1+(\sqrt{7})^{2}}=\frac{1}{1+7}=\frac{1}{8}\\\\8Cos^{4}\alpha-8Cos^{2}\alpha+1=8*(\frac{1}{8})^{2}-8*\frac{1}{8}+1=\frac{1}{8}-1+1=\frac{1}{8}=0,125$