6cos^2x+7sinx-8=0
6(1-sin^2x)+7sinx-8=0
6-6sin^2x+7sinx-8=0
6sin^2x-7sinx+2=0 замена переменной sinx =t ; -1=< t =<1
6t^2-7t+2=0
D =49-48=1
t1 =1/2 ; sinx =t1 =1/2= sin(2pi*n+pi/6)=sin(2pi*n+5pi/6), n ϵ Z
t2=2/3 ; sinx =t2 =2/3= sin(2pi*n+pi-1/sin(2/3))=sin(2pi*n+1/sin(2/3), n ϵ Z
ОТВЕТ
х=(2pi*n+pi/6), n ϵ Z
х=(2pi*n+5pi/6), n ϵ Z
х=(2pi*n+pi-1/sin(2/3)), n ϵ Z
х=(2pi*n+1/sin(2/3), n ϵ Z
6cos^2x+7sinx-8=0
6(1-sin^2x)+7sinx-8=0
6-6sin^2x+7sinx-8=0
6sin^2x-7sinx+2=0 замена переменной sinx =t ; -1=< t =<1
6t^2-7t+2=0
D =49-48=1
t1 =1/2 ; sinx =t1 =1/2= sin(2pi*n+pi/6)=sin(2pi*n+5pi/6), n ϵ Z
t2=2/3 ; sinx =t2 =2/3= sin(2pi*n+pi-1/sin(2/3))=sin(2pi*n+1/sin(2/3), n ϵ Z
ОТВЕТ
х=(2pi*n+pi/6), n ϵ Z
х=(2pi*n+5pi/6), n ϵ Z
х=(2pi*n+pi-1/sin(2/3)), n ϵ Z
х=(2pi*n+1/sin(2/3), n ϵ Z