1) 5cos2x-42sinx-13=0
2) 11sin2x-6cos^2x-4=0

Спасибо большое

1) 5cos2x -42sinx -13 =0 ;5(1-2sin²x) - 42sinx -13 =0 ;10sin²x) + 42sinx +8 =0 ;5sin²x) + 21sinx +4 =0 ;  * * * замена  t =sinx ;  |t| ≤1 . * * *5t² +21t +4 = 0 ; * * * D =21² -4*5*4 =441- 80 =361 =19² * * *t₁ =(-21-19)/2*5 = -4  * * * |t₁| = |-4| = 4> 0 . * * *t₁ =(-21+19)/2*5 = -2/10 = -1/5. [ sinx =- 4  ; sinx = -1/5.sinx = -1/5 ;x =(-1)^(n+1)arcsin(1/5) +πn , n∈Z.-------2) 11sin2x-6cos²x-4=0 ;22sinxcosx -6cos²x -4(sin²x +cos²x) =0 ;2sin²x -11sinx*cosx  + 5cos²x =0 ;2tq²x - 11tqx  + 5 =0 ; * * * замена  t =tqx ; * * *2t² - 11t  + 5 =0  ; * * * D =11² -4*2*5 =121- 40 =81 =9² * * *[ t =(11- 9)/4=1/2; t =(11+9)/4=5.tqx =1/2 ⇒ x =arctq(1/2) +πn ,n∈Z.t =5   ⇒   x =arctq5 +πn ,n∈Z.