SSC CGL 2024 PYQ — Question 60

The correct answer is option 3 i.e. 5.

${5\over1+cot^2 \theta} + {3\over1+tan^2 \theta} + 2cos^2\theta$

= (5/cosec²θ) + (3/sec²θ) + 2cos²θ   [∵ 1 + cot²θ = cosec²θ and 1 + tan²θ = sec²θ]

= 5sin²θ + 3cos²θ + 2cos²θ

= 5sin²θ + 5cos²θ

= 5(sin²θ + cos²θ)

= 5 × 1   [∵ sin²θ + cos²θ = 1]

= 5

Therefore, the value of the expression is 5.