If sinθ + cosec θ = 5 , find the value of sin3θ + cosec3θ.
Answer & explanation
Correct answer: option 3
Formula I → [cosec = \(\frac{1}{sinθ}\)]
Formula II → [If x + \(\frac{1}{x}\) = n and x3 + \(\frac{1}{x^3}\) = n3 - 3n]
sinθ + \(\frac{1}{sinθ}\) = 5
⇒ sin3θ + \(\frac{1}{sin^3θ}\) = (5)3 - 3 × 5
⇒ sin3θ + cosec3θ = 125 - 15 = 110