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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)

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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) 

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