If ,then

The correct answer is:

Here , we have to find where θ lies in this equation.
Firstly, we have given

We know that,


= 1 + 2 sin θ cos θ
So, we can write, in eq (1)

sin θ cos θ - |sin θ| cos θ = 0
cos θ ( sin θ - | sin θ| ) = 0
hence, sin θ = | sin θ |
which is always true for sinx ≥ 0 otherwise it is true for x=0,,,2π
Therefore, since we also need x≠, for tanx and x≠0,2π for cotx all the solutions are given by x∈(0,π) with x≠and x≠.
The correct answer is θ ϵ (0 ,π)- { ,}

In this question, we have to find the where is θ lies. Here, always true for sinx ≥ 0 otherwise it is true for x=0,,,2π and since we also need x≠, for tanx and x≠0,2π for cotx all the solutions.