Question

Solve: {[sec(90° - A) × cosec A] / sin²(90° - A)} × cos ²A
1. (1/cos A)
2. (1/cosec A)
3. (1/sin²A)
4. (1/tan A)

Answer 1

Correct Answer - Option 3 : (1/sin²A)

Given

{[sec(90° - A) × cosec A]/sin2(90° - A)} × cos²A

Formula used

sec(90° - A) = cosec A

sin(90° - A) = cos A

cosec A = 1/sin A

Calculation

{[sec(90° - A) × cosec A]/sin2(90° - A)} × cos²A

⇒ [(cosecA × cosec A)/cos ²A] × cos² A

⇒ (cosec²A/cos² A) × cos² A

⇒ cosec²A

⇒ (1/sin²A)

∴ {[sec(90 - A) × cosec A]/sin2(90 - A)} × cos ²A is (1/sin²A)