If x-1-x-2 cos- then x3-1-x3-MP PET 2004-

The correct option is B We have x + nbsp; 1/x = 2cosθ, Now x^3 + nbsp; 1/x^3 = (x + 1/x)^3 3x 1/x(x + 1/x) = (2 cosθ)^3 3(2 cosθ) = 8 cos^3 θ 6 cosθ ...

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Byju's Answer

Standard XII

Mathematics

Circular Measurement of Angle

If x+1/x=2 co...

Question

If x + $\frac{1}{x}$ = $2 c o s θ$ , then $x^{3}$ + $\frac{1}{x^{3}}$ =

[MP PET 2004]

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Solution

The correct option is B

We have x + $\frac{1}{x}$ = $2 c o s θ$ ,

Now $x^{3}$ + $\frac{1}{x^{3}}$ = ${(x + \frac{1}{x})}^{3}$ - $3 x \frac{1}{x} (x + \frac{1}{x})$

= $(2 c o s θ)^{3} - 3 (2 c o s θ) = 8 c o s^{3} θ - 6 c o s θ$

= $2 (4 c o s^{3} θ - 3 c o s θ) = 2 c o s 3 θ$ .

Trick: Put x = 1 $\Rightarrow$ $θ = 0^{\circ}$ .

Then $x^{3}$ + $\frac{1}{x^{3}}$ = 2 = $2 c o s 3 θ$ .

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Similar questions

If x + $\frac{1}{x}$ = $2 c o s θ$ , then $x^{3}$ + $\frac{1}{x^{3}}$ =

Q. If

x + \frac{1}{x} = 2 cos θ,

then

x^{3} + \frac{1}{x^{3}} =

Q. If

x + \frac{1}{x} = 2 c o s θ, t h e n x^{3} + \frac{1}{x^{3}} =

Q. If

x + \frac{1}{x} = 2 cos θ,

then find the value of

x^{3} + \frac{1}{x^{3}} .

Q. If

2 cos θ = x + \frac{1}{x}

, then prove that

2 cos 3 θ = x^{3} + \frac{1}{x^{2}}

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If x + 1x = 2cosθ, then x3 + 1x3 = [MP PET 2004]

The correct option is B We have x + 1x = 2cosθ, Now x3 + 1x3 = (x+1x)3 - 3x1x(x+1x) = (2cosθ)3−3(2cosθ)=8cos3θ−6cosθ =2(4cos3θ−3cosθ)=2cos3θ. Trick: Put x = 1 ⇒ θ=0∘. Then x3 + 1x3 = 2 = 2cos3θ.

If x + $\frac{1}{x}$ = $2 c o s θ$ , then $x^{3}$ + $\frac{1}{x^{3}}$ =

[MP PET 2004]