My first approach for this question is that since we have to count for real roots so we will find D which is equal to 0 and we can interpret that the roots will always be zero no matter what value of cos x we take. so probability is 1 here and we get m + n = 2.
And there is one more approach that this original equation can be written as (2 cos x + 1)² = 0, from here since x is equal to 2π/3 is the only valid solution and getting this x from that range will tend to 1/∞ which is equal to 0 = 0/1 and so m + n = 1.
My doubt is which approach is wrong and why? Thanks in advance.
