4cosxsin2xsinx=1 4sinxcox+1=0 tgx≤1 √2sin3x=1 sin3x=sin5x y=3-4sin²xcos2x

1) 4sinx*cosx*sin2x =1 ; 2sin2x*sin2x =1 ; sin²2x =1/2 ; ( 1 -cos4x) /2 =1/2 ;  1 -cos4x =1 ; cos4x =0 ⇒ 4x =π/2 +π*K⇒ x =π/8 +(π/4)*k ; k∈Z. ----------------------- 2) tg x≤ 1 ;   - π*k - π/2 ≤ x ≤  π/4  + π*k . 3) √2sin3x=1 ; sin 3x =1/√2 ; 3x =(-1)^k*π/4 +2π*k ; x =(-1)^k*π/12 +2π*k ; k ∈Z .. 4)  sin3x=sin5x ; sin5x - sin3x =0 ; 2sin(5x - 3x)/2 *cos(5x + 3x)/2 =0 ; 2sinx *cos4x =0 ; [ sinx =0 ; cos4x =0⇒[x =π*k ; 4x= π/2+π*k . [x =π*k ; x= π/8+π/4*k ;k ∈Z .