If $x+\frac{1}{x}= 2 cos θ$, then

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

If $x+\frac{1}{x}= 2 cos θ$, then $x^3 +\frac{1}{x^3}=$?

Options:

2 cos 2θ

cos 3θ

2 cos 3θ

cos 2θ

Correct Answer:

2 cos 3θ

Explanation:

If $x+\frac{1}{x}= 2 cos θ$,

then $x^3 +\frac{1}{x^3}=$?

Put cosθ = 0^o

cos0^o = 1

then,

$x+\frac{1}{x}= 2$

$x^3 +\frac{1}{x^3}=$ 2³ - 2 × 3 = 2

Satisfy from the options = 2 cos 3θ = 2cos0^o = 2 satisfied.

So the value of $x^3 +\frac{1}{x^3}$ = 2 cos 3θ