The value of cosec² 18°

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The value of cosec² 18° – 1 is
cot² 72°

1. 1
  √3
2. √2
  3
3. 1
  2
4. 1

Correct Option: D

Expression

= cosec² 18° -	1
	cot²72°

= cosec² 10° - tan² 72°
[∵ tan θ . cot θ = 1]
= cosec²18° – tan²(90° – 18°)
= cosec² 18° – cot² 18° = 1
[∵ tan (90° – θ = cot θ ; cosec² θ – cot² θ = 1]

	1
	√3

	√2
	3