SSC CHSL 2021 PYQ — Question 57

The correct answer is option 4 i.e. -1.

$Cosec \theta = \frac{1}{Sin \theta }$

$Sin^2 \theta+ Cos^2 \theta = 1$

$(a + b)(a - b) = a^2 - b^2$

cosec² θ (cos θ - 1)(1 + cos θ) = k

⇒ cosec² θ (1 - cos θ)(1 + cos θ) = -k

⇒ cosec² θ (1 - cos² θ) = -k

⇒ cosec² θ × sin² θ = -k

⇒ 1 = -k

⇒ k = -1