Very hard math question?

Question

cos(x)/tan(x) = M 
Find x in terms of M.

Answer 1

The equation cos(x)/tan(x) = M

cos(x) cot(x) = M

cos(x) [cos(x)/sin(x)] = M

cos²(x)/sin(x) = M

(1 - sin²x )/sinx = M

1 - sin²x = Msin(x)

(sin(x))² + M sin(x) - 1 = 0

Let sin(x) = X

Now the equation becomes

Compare it to quadratic form

Roots are

Back substitute X = sin(x)

.