6*cos^2(x)+7*sin(x)-8 = 0

Question

6*cos^2(x)+7*sin(x)-8 = 0

Answer 1

6(1-sin^2)+7sinx-8=0

6-6sin^2x+7sinx-8=0

6sin^2x-7sinx+2=0

sinx=y

6y^2-7y+2=0

D=49-48=1

x1=2/3

x2=1/2

1)sinx=2/3

x=(-1)^n*arcsin2/3+Пn

2)sinx=1/2

x=(-1)^n*arcsin1/2+Пn

x=(-1)^n*П/6+Пn