Question

2sin^2 4x-4=3sin4xcos4x-4cos^2 4x

Answer 1

$2sin^2 4x-4=3sin4xcos4x-4cos^2 4x\ 2sin^2 4x-4*1=3sin4xcos4x-4cos^2 4x\ 2sin^2 4x-4sin^24x-4cos^24x=3sin4xcos4x-4cos^2 4x\ -2sin^2 4x=3sin4xcos4x\ 2sin^2 4x+3sin4xcos4x=0\ sin4x(2sin4x+3cos4x)=0\ sin4x=0 2sin4x+3cos4x=0\ 4x= pi k, k in Z\ x= frac{ pi k}{4} , k in Z\ 2sin4x+3cos4x=0|:cos4x\ 2tg4x+3=0\ tg4x=-1,5\ 4x=arctg(-1,5)+ pi k, k in Z\ 4x=-arctg1,5+ pi k\ x=- frac{1}{4} arctg1,5+ frac{ pi k}{4} , k in Z$