If sec15θ = cosec15θ (0° < θ < 10°) then the value of θ is?

Answer: Option D

$$\begin{array}{rl}& \sec 15\theta =\mathrm{cosec}15\theta \\ & \Rightarrow \frac{1}{\cos 15\theta }=\frac{1}{\sin 15\theta }\\ & \Rightarrow \frac{\sin 15\theta }{\text{cos15}\theta }=1\\ & \Rightarrow \text{tan15}\theta =1\\ & \Rightarrow \text{tan15}\theta =\text{tan}45^{\circ }\\ & \Rightarrow 15\theta =45^{\circ }\\ & \Rightarrow \theta =\frac{45}{15}\\ & \Rightarrow \theta =3^{\circ }\end{array}$$