Question

0.5×sin2x×ctgx-cosx=sin^2x

Answer 1

ctgx=cosx/sinx
sin2x=2sinx*cosx

0.5*sin2x*ctgx - cosx = sin^2 x

0.5*2*sinx*cosx*cosx/sinx - cox = 1 - cos^2 x

cos^2 x - cosx - 1 + cos^2 x =0

2cos^2 x - cosx - 1 = 0

cosx = t

2t^2 - t - 1 = 0
D=1-4*2*(-1)=9
t1=1
t2=-0.5
1. cosx=1
2. cosx=-0.5
отсюда находим х