If sinθ - cosec θ = 7 , find the value of sin3θ - cosec3θ .
Answer & explanation
Correct answer: option 2
Formula I → [ cosecθ = \(\frac{1}{sinθ}\)]
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 = 364