If tan 2θ . tan 3θ = 1, where 0° < θ

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If tan 2θ . tan 3θ = 1, where 0° < θ < 90° then the value of θ is

1. 22 1 °
  2
2. 18°
3. 24°
4. 30°

Correct Option: B

tan2θ . tan3θ = 1

⇒ tan3θ =	1	= cot2θ
	tan2θ

⇒ tan3θ = tan (90° – 2θ)
⇒ 3θ = 90° – 2θ
⇒ 3θ + 2θ = 5θ = 90°

⇒ θ =	90°	= 18°
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