Question

Найти cos2a если (cosa-2sina)/(sina-2cos)=-0.5

Answer 1

$\frac{cosa-2sina}{sina-2cosa} =-0,5\; ,\; \; \; cos2a=?\\\\ \frac{cosa-2sina}{sina-2cosa} =\Big [\frac{:cosa}{:cosa} \Big ]= \frac{1-2tga}{tga-2} =-0,5\\\\1-2tga=-0,5(tga-2)\\\\1-2tga=-0,5tga+1\\\\1,5tga=0\; \; \; \to \; \; \; tga=0\\\\Formyla:\; \; \; cos2a= \frac{1-tg^2a}{1+tg^2a} \\\\cos2a= \frac{1-0}{1+0} =1$