Correct Answer - Option 3 : (1/sin

^{2}A)

**Given**

{[sec(90° - A) × cosec A]/sin2(90° - A)} × cos^{2}A

**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)} × cos^{2}A

⇒ [(cosecA × cosec A)/cos ^{2}A] × cos^{2} A

⇒ (cosec^{2}A/cos^{2} A) × cos^{2} A

⇒ cosec^{2}A

⇒ (1/sin^{2}A)

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