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Question

If cos θ=12(a+1a), and cos 3θ=λ(a3+1a3), then λ=


  1. 14

  2. 12

  3. 1

  4. none of these


Solution

The correct option is B

12


Given:

cos θ=12 (a+1a)cos 3θ=λ(a3+1a3)

Now,

cos3θ=18 [a3+1a3+3a1a(a+1a)]    cos3 θ=18 (a3+1a3+3×2 cos θ)[  cos θ=12 (a+1a)]  cos3 θ=18 (cos 3 θλ+6 cos θ)   cos3 θ=18 (4 cos2 θ3 cos θλ+6 cos θ)   cos3 θ=4 cos2 θ8λ3 cos θ8 λ+6 cos θ8

On comparing the power of cos3 θ on both sides, we get 1=44λ

  λ=12

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