TS EAMCET 2017 Code A Solved Paper

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