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  1. If sinθ + cosecθ = 2, then value of sin100θ + cosec100θ is equal to :
    1. 1
    2. 2
    3. 3
    4. 100
Correct Option: B

sinθ + cosecθ = 2

⇒ sin θ +
1
= 2
sin θ

⇒ sin2θ – 2 sinθ + 1 = 0
⇒ (sinθ – 1) = 0
⇒ sinθ = 1 ⇒ cosecθ = 1
∴ sin100θ + cosec100θ
= 1+ 1 = 2


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