Question

Найдите (2cos^2a-sin 2a)/(2sin^2a-sin 2a) если tga=-1/4

Answer 1

$cfrac{2cos^2 alpha -sin2 alpha }{2sin^2 alpha -sin2 alpha }= cfrac{2cos^2 alpha -2sin alpha cos alpha }{2sin^2 alpha -2sin alpha cos alpha }= cfrac{2cos alpha (cos alpha -sin alpha )}{2sin alpha (sin alpha -cos alpha )} = \ \ \ = cfrac{cos alpha (cos alpha -sin alpha )}{-sin alpha (cos alpha -sin alpha )} =- ctg alpha \ \ \ tg alpha cdot ctg alpha =1 \ \ ctg alpha = cfrac{1}{tg alpha } \ \ ctg alpha = cfrac{1}{- frac{1}{4} }=-4$

$-ctg alpha =-(-4)=4$

Answer 2

норм