Question

вычислите 2sin^2x-5sinxcosx=3

Answer 1

$2sin^2x-5sinxcosx=3 2sin^2x-5sinxcosx-2-1=0 (-1) -2sin^2x+5sinxcosx+2+1=0 (1-2sin^2x)+5sinxcosx+2=0 cos^2x-sin^2x+5sinxcosx+2=0 (cos^2x-sin^2x+2sin^2x+2cos^2x)+5sinxcosx=0 sin^2x+cosx^2x+5sinxcosx=0 (delim na cos^2x) tg^2x+1+5tgx=0 pyst tgx=t t^2+5t+1=0 t1/2=(-5+- \sqrt{25-4})/2 t1=(-5- \sqrt{21})/2 t2=(-5+ \sqrt{21})/2$