Question

1,6,8 помогите пожалуйста

Answer 1

$1)\; \; cos2a=\frac{2}{3}\\\\cos^2a=\frac{1+cos2a}{2}=\frac{1+\frac{2}{3}}{2}=\frac{5}{6}\\\\6)\; \; \frac{ctg^2a-1}{cos2a}=\frac{\frac{cos^2a}{sin^2a}-1}{cos2a}=\frac{\frac{cos^2a-sin^2a}{cos^2a}}{cos2a}= \frac{cos^2a-sin^2a}{cos^2a\cdot cos2a}=\\\\=\frac{cos2a}{cos^2a\cdot cos2a}=\frac{1}{cos^2a} \\\\8)\; \; (cosa+sina)^2+sin2a=\\\\=cos^2a+\underbrace {2sina\cdot cosa}_{sin2a}+sin&2a+sin2a=\\\\=(\underbrace {sin^2a+cos^2a}_{1})+sin2a+sin2a=1+2sin2a$