1)
begin{lgathered}cos^{2}x+2cosx-3=0\ cosx=t\ t^{2}+2t-3=0\ D=4+12=16\ t1=1\ t2=-3\ cosx=1\ x=2pi kend{lgathered}cos2x+2cosx−3=0cosx=tt2+2t−3=0D=4+12=16t1=1t2=−3cosx=1x=2πk
2)
begin{lgathered}2tg^{2}x+3tgx-2 = 0\ tgx=t\ 2t^{2}+3t-2=0\ D = 9+16=25\ t1 = frac{-3+5}{4} = frac{1}{2}\ t2 = -2\ tgx=frac{1}{2}\ x=arctgfrac{1}{2}+pi k\ tgx=-2\ x=-arctg2+pi kend{lgathered}2tg2x+3tgx−2=0tgx=t2t2+3t−2=0D=9+16=25t1=4−3+5=21t2=−2tgx=21x=arctg21+πktgx=−2x=−arctg2+πk )