Question

Доказать тождество
1-2cos2^a/sinacosa=tga-ctga

Answer 1

$frac{1-2cos^2a}{sinxcdot cosx} =Big [cos^2a= frac{1+cos2a}{2}; ; to ; ; 2cos^2a=1+cos2a; Big ]=\\= frac{1-(1+cos2a)}{sinacdot cosa} = frac{-cos2a}{sinacdot cosa} = frac{-(cos^2a-sin^2a)}{sinacdot cosa} = -frac{cos^2a}{sinacdot cosa} +frac{sin^2a}{sinacdot cosa} =\\ =-frac{cosa}{sina} +frac{sina}{cosa} =-ctga+tga=tga-ctga$