SSC CHSL 2021 PYQ — Question 73

The correct answer is option 3 i.e. 3

$(cos^2\theta-1)(2sec^2\theta) + sec²\theta+2tan^2\theta=2,0° <\theta< 90°$

- sin²θ * 2/cos²θ  + sec²θ + 2tan²θ = 2

- 2 tan²θ + sec²θ + 2tan²θ = 2

sec²θ = 2

sec θ = √2

θ = 45º

Now, $\frac{(sec\theta + sin\theta)}{(cosec\theta-cos\theta)}$

$\frac{(sec\ 45 + sin\ 45)}{(cosec\ 45-cos\ 45)}$ = $\frac{\sqrt2 + (1/\sqrt2)}{\sqrt2-(1/\sqrt2)}$ = 3