If sinθ + cosec θ = 7, find the value of sin3θ + cosec3θ.

322 382 365 350

322

Formula I → [cosec = \(\frac{1}{sinθ}\)] Formula II → [If x + \(\frac{1}{x}\) = n and x3 + \(\frac{1}{x^3}\) = n3 - 3n] sinθ + \(\frac{1}{sinθ}\) = 7 ⇒ sin3θ + \(\frac{1}{sin^3θ}\) = (7)3 - 3 × 7 ⇒ sin3θ + cosec3θ = 343 - 21 = 322