Consider the given trigonometric equation cosec‌θ−cot‌θ=2017.....(1) We know that, cosec2θ−cot2θ=1 (cosecθ−cot‌θ)(cosecθ+cot‌θ)=1 cosecθ+cot‌θ=‌‌
1
cosecθ−cot‌θ
cosecθ+cot‌θ=‌‌
1
2017
.....(2)Add equation (1) and (2). 2‌cosec‌θ=2017+‌‌
1
2017
cosecθ=‌‌
1
2
[2017+‌‌
1
2017
]>0 Therefore, θ lies in I or II quadrant. Subtracting equation (1) from (2), 2‌cot‌θ=‌‌
1
2017
−2017 cot‌θ=‌‌
1
2
(‌‌
1
2017
−2017)<0 Therefore, θ lies in II and III quadrant. Hence, theta lies in II quadrant