UPSC NDA Math Model Paper 8

Here, sin θ - cos θ = -2 .....(1)
⇒1/cosec θ - 1/sec θ = -2
⇒ sec θ - cosec θ = -2 sec θ cosec θ ....(2)
Now, sec θ cosec θ = 1/sin θ cos θ = 2/sin 2θ
So, equation (2) becomes
sec θ - cosec θ = 2/sin 2θ .....(3)
Squaring equation (1), we get
sin2θ + cos2θ - 2sin θ cos θ = 4 1 - sin 2θ = 4
⇒ sin 2θ = -3 ...(4)
From (3) and (4)
sec θ - cosec θ = -2/3
Hence, option (2) is correct.