If x + (1/x) = 2 cos θ , then x3 + (1/x3) is :

Question

If x + (1/x) = 2 cos θ , then x3 + (1/x3) is : (A) (1/2) cos 3 θ (B) 2 cos 3 θ (C)  cos 3 θ  (D) (1/3) cos 3 θ

Tardigrade Admin · Accepted Answer

Given: x + (1/x) = 2 cos θ ....(1) Cubic both sides in eqn (1) we get x3 + (1/x3) + 3 (x+ (1/x)) = 8 cos3 θ ⇒ x3 + (1/x3 ) + 3(2 cosθ) = 8 cos3 θ ⇒ x3 + (1/x3) = 8 cos3 θ - 6 cosθ ⇒ x3 + (1/x3 ) = 2(4 cos3 θ - 3 cosθ) = 2 cos3 θ

Q. If $x + \frac{1}{x} = 2 cos θ$ , then $x^{3} + \frac{1}{x ^{3}}$ is :

$\frac{1}{2} cos 3 θ$

$2 cos 3 θ$

$cos 3 θ$

$\frac{1}{3} cos 3 θ$

Q. If x+x1​=2cosθ, then x3+x31​ is :

21​cos3θ

2cos3θ

cos3θ

31​cos3θ

Given : x+x1​=2cosθ ....(1) Cubic both sides in eqn (1) we get x3+x31​+3(x+x1​)=8cos3θ ⇒x3+x31​+3(2cosθ)=8cos3θ ⇒x3+x31​=8cos3θ−6cosθ ⇒x3+x31​=2(4cos3θ−3cosθ)=2cos3θ

Q. If $x + \frac{1}{x} = 2 cos θ$ , then $x^{3} + \frac{1}{x ^{3}}$ is :

$\frac{1}{2} cos 3 θ$

$2 cos 3 θ$

$cos 3 θ$

$\frac{1}{3} cos 3 θ$