Question

срочно решите, оч надо

Answer 1

$1)Cos\alpha=Cos^{2}\frac{\alpha}{2}-Sin^{2}\frac{\alpha}{2}\\\\Cos\alpha=2Cos^{2}\frac{\alpha}{2}-1\\\\Cos\alpha=1-2Sin^{2}\frac{\alpha}{2}$

$2)Sin3\alpha=2Sin\frac{3\alpha}{2}Cos\frac{\alpha}{2}$

$3)tg\frac{\alpha}{2}=\frac{2tg\frac{\alpha}{4}}{1-tg^{2}\frac{\alpha}{4}} \\\\4)Cos8\alpha=Cos^{2}4\alpha-Sin^{2}4\alpha\\\\Cos8\alpha=2Cos^{2}4\alpha-1\\\\Cos8\alpha=1-2Sin^{2}4\alpha$

$5)Sin(2x-\frac{\pi}{6})=2Sin(x-\frac{\pi}{12})Cos(x-\frac{\pi}{12})\\\\6)tg7\alpha=\frac{2tg3,5\alpha}{1-tg^{2}3,5\alpha}\\\\7)Sin(\alpha-\beta)=2Sin\frac{\alpha-\beta}{2}Cos\frac{\alpha-\beta }{2}\\\\8)tg3=\frac{2tg1,5}{1-tg^{2}1,5 }$