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      Question

      If x+  1/x = 2cosθ, then the value of x³+  1/x³

      is
      A 2cos2θ Correct Answer Incorrect Answer
      B 2cos3θ Correct Answer Incorrect Answer
      C 2sin2θ Correct Answer Incorrect Answer
      D 2sin2θ Correct Answer Incorrect Answer

      Solution

       x+  1/x = 2cosθ  (x+  1/x)³ = (2cosθ)³ x³+  1/x³+ 3x ×  1/x  ×(x+  1/x) = 8cos³θ x³+  1/x³+ 3 ×2cosθ = 8cos³θ x³+  1/x³ = 8cos³θ - 6cosθ x³+  1/x³ = 2(4cos³θ-3cosθ) Using identity  [4cos³θ-3cosθ=cos3θ] x³+  1/x³ = 2cos3θ  

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