If sinq+ cosecθ = 2, then the value of (sin-7θ

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If sinq+ cosecθ = 2, then the value of (sin^-7θ + cosec⁷θ) is

1. 2⁷
2. 2^-7
3. 2
4. 2^-1

Correct Option: C

sinθ + cosecθ = 2
⇒ sinθ + 1/sinθ = 2
⇒ sin2θ + 1 = 2sinθ
⇒ sin²θ – 2sinθ + 1 = 0
⇒ (sinθ – 1)² = 0
⇒ sinθ – 1 = 0
⇒ sinθ = 1
∴ cosecθ = 1
∴ sin^-7θ + cosec⁷θ
= (1)^-7 + (1)⁷ = 2