sinθ + cosecθ = 2 হলে, sin⁵θ + cosec⁵θ = কত?

প্রশ্ন: sinθ + cosecθ = 2 হলে, sin⁵θ + cosec⁵θ = কত?

সমাধান:
sinθ + cosecθ = 2
বা, sinθ + 1/sinθ = 2
বা, (sin²θ + 1)/sinθ = 2
বা, sin²θ + 1 = 2 sinθ
বা, sin²θ - 2sinθ + 1 = 0
বা, (sinθ - 1)² = 0
বা, sinθ - 1 = 0
∴ sinθ = 1

∴ cosecθ = 1/sinθ
= 1/1
= 1

∴ sin⁵θ + cosec⁵θ
= (1)⁵ + (1)⁵
= 1 + 1
= 2