4^3cos^2 x-2sinx-2 =1

Question

4^3cos^2 x-2sinx-2 =1

Comments

4^(3cos²x -2sinx -2) =1 может так?

Answer 1

4^(3cos²x -2sinx -2) =1 ;
4^(3cos²x -2sinx -2) =4⁰ ;
3cos²x -2sinx -2 =0 ;
3(1-sin²x) -2sinx -2 =0 ;
3sin²x +2sinx -1 =0 ; * * * t =sinx ; |t| ≤1 * * *
3t² +2t -1 =0 ; * * * D/4 =(-1)² -3*(-1) =4 =2²  * * *
3t² +2t -1 =0 ; * * * D/4 =(-1)² -3*(-1) =4 =2²  * * *
t₁ =(-1-2)/3 =-1 ;
t₁ =(-1+2)/3 =1/3.
[ sinx = -1 ; sinx =1/3. ⇒[ x = -π/2+2πn ; x =(-1)^n *arcsin(1/3) +πn ,n∈Z.