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Question

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

A
cos 3θ
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B
2 cos 3θ
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C
12cos 3θ
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D
13cos 3θ
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Solution

The correct option is B 2 cos 3θ
We have x+1x=2cosθ,
Now, using the identity:
a3+b3=(a+b)33ab(a+b)

x3+1x3=(x+1x)33x×1x(x+1x)

x3+1x3=(2cosθ)33×2cosθ

x3+1x3=8cos3θ6cosθ
x3+1x3=2(4cos3θ3cosθ)
x3+1x3=2cos3θ

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