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  1. If tan 3θ. tan 7θ = 1, then the value of tan (θ + 36°) is :
    1. 1
      √3
    2. 0
    3. 1
    4. √3
Correct Option: C

tan 3θ. tan 7θ = 1

⇒  tan 3θ =
1
 = cot7θ
tan 7θ

⇒  tan3θ = tan (90° – 7θ)
⇒  3θ = 90° – 7θ
⇒  3θ + 7θ = 90°
⇒  10θ = 90° ⇒ θ = 9°
∴  tan (θ + 36°) = tan (9° + 36°)
= tan 45° = 1


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