This question was previously asked in

Territorial Army Paper I : Official Practice Test Paper - 2

Option 3 : \(\dfrac{\pi}{4}\)

**Concept used**

Cosec^{2}θ - cot^{2}θ = 1

**Calculation**

\(\dfrac{cos x}{1+cosecx}+\dfrac{cos x}{cosec x - 1}=2\)

\(\cos x\left( {\frac{1}{{\cosec x + 1}} + \frac{1}{{\cosec x - 1}}} \right) = 2\)

\(\cos x\left( {\frac{{\cosec x - 1 + \cosec x + 1}}{{(\cosec x + 1)(\cosec x - 1)}}} \right) = 2\)

\(\frac{{2\cos x.\cosec x}}{{\cose{c^2}x - 1}} = 2\)

\(\frac{{2\cos x.\cosec x}}{{{{\cot }^2}x }} = 2\)

\(\frac{{\cos x \times 2}}{{\sin x}} \times \frac{{{{\sin }^2}x}}{{co{x^2}x}} = 2\)

Tan x = 1

Tan x = π/4

x = \(\dfrac{\pi}{4}\)