Question

sin2x+2cos2x=1

Answer 1

2sinx*cosx+2cos^2x-2sin^2x=sin^2x+2cos^2x, -3sin^2x+2sinx*cosx+cos^2x=0, разделим все н (-cos^2x), 3tg^2x-2tgx-1=0, tgx=a, 3a^2-2a-1=0, a1=1, a2=-1/3. tgx=1, x=п/4+пk,kєZ, tgx=-1/3, x= -arctg(1/3)+nl, lєZ.