Question

2cos квадрат x-5cos x-3=0

Answer 1

$displaystyle 2cos^2x-5cosx-3=0 ;big| cosx=t\\2t^2-5t-3=0\\D:25+24=1\\t_1,_2=frac{5pm1}{4}; quad x_1=frac{3}{2}, quad x_2=1;\\1. ; cosx neq frac{3}{2}, ; cosx in [-1;1];\\2. ; cosx=1\x=2pi n, ; nin Z.$