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If sinθ + cosec θ = 4 , find the value of sin3θ + cosec3θ . |
48 62 52 58 |
52 |
Formula I → [ cosec = \(\frac{1}{sinθ}\)] Formula II → [If x + \(\frac{1}{x}\) = n and x3 + \(\frac{1}{x^3}\) = n3 - 3n] sinθ + \(\frac{1}{sinθ}\) = 4 ⇒ sin3θ + \(\frac{1}{sin^3θ}\) = (4)3 - 3 × 4 ⇒ sin3θ + cosec3θ = 64 - 12 = 52 |
