If x-1-x-2 cos- then x3-1-x3-A- 2 cos 3 -B- cos 3 -C- 1-3cos 3 -D- 1-2cos 3 -

The correct option is A We have x+1/x=2 cos θ, Now x^3+1/x^3=(x+1/x)^3 3x1/x(x+1/x) =(2 cos θ)^3 3(2 cos θ)=8 cos^3 θ 6 cos θ =2(4 cos^3 θ 3 cos θ)=2 cos 3θ. T ...

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Byju's Answer

Standard XI

Mathematics

Trigonometric Ratios of Multiples of an Angle

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

Question

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

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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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If x+1x=2 cos θ, then x3+1x3=

The correct option is B We have x+1x=2 cos θ, Now x3+1x3=(x+1x)3−3x1x(x+1x) =(2 cos θ)3−3(2 cos θ)=8 cos3 θ−6 cos θ =2(4 cos3 θ−3 cos θ)=2 cos 3θ. Trick: Put x=1⇒θ=0∘. Then x3+1x3=2=2 cos 3θ.

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