Solve for y 11 sin^2y=13-sin^2y where 0 < y < 360.
Add sin^2y to both sides of the equation:
11sin^2y +sin^2y = 13-sin^2y+sin^2y.
12sin^2y = 13.
sin^2y = 13/12.
But sin^2y > 1 is not admissible as the siney functin is defined only for -1 <= siny <= 1, sin^2 y > 1 is not possible. There is no solution for y.
The first step is to isolate (sin y)^2 to the left side. For this reason, we'll add (sin y)^2 both sides:
11 (sin y)^2 + (sin y)^2 = 13
12 (sin y)^2 =13
We'll divide by 12:
(sin y)^2 = 13/12
sin y = sqrt (13/12)
But sqrt (13/12)>1 and -sqrt (13/12) < -1, which is impossible because the limit values of the sine function are -1 and 1.
So, there are no angles to satisfy the given equation, or, more precise, the equation has no solution.