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Question

If cos x=12 a+1a, and cos 3 x = λ a3+1a3, then λ=
(a) 14

(b) 12

(c) 1

(d) none of these

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Solution

(b) 12
Given:cosx=12a+1a cos3x=λa3+1a3Now,cos3x=18a3+1a3+3a1aa+1acos3x=18a3+1a3+3×2cosx cosx=12a+1acos3x=18cos3xλ+6cosxcos3x=184cos3x-3cosxλ+6cosxcos3x=4cos3x8λ-3cosx8λ+6cosx8On comparing the powers of cos3x on both sides, we get1=48λλ=12

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