If the equation `sin^2 x-a sin x + b = 0` has only one solution in `(0, pi)` then which of the following statements are correct?

Solve the equation sin^2 x - 5 sin x + 4 = 0

The equation 2 sin ^ 2 x + 7 sin x + 6 =0 has

If the equation x^2=a x+b=0 has distinct real roots and x^2+a|x|+b=0 has only one real root, then which of the following is true? b=0, a >0 b. b=0, a 0, a >0

If the equation sin ^(2) x - k sin x - 3 = 0 has exactly two distinct real roots in [0, pi] , then find the values of k .

If equation x^2+2x+2 + e^alpha - 2 sin beta = 0 has a real solution in x, then (where n in ZZ )

Prove that the equation 2 sin x=|x|+a has no solution for a in ((3sqrt(3)-pi)/3, oo) .

If the equation a sin^(3)x+(b-s)sin^(2)x+(c-b)sin x=c =0 has exactly three distinct solutions in [0, pi] , where a + b + c = 0, then which of the following is not the possible value of c/a ?

For x in (0,pi), the equation sinx+2 sin 2x-sin3x=3 has (A)infinitely many solutions (B)three solutions (C)one solution (D)no solution

If the equation x^(2)+12+3sin(a+bx)+6x=0 has atleast one real solution, where a, b in [0,2pi] , then the value of a - 3b is (n in Z)