If x+(1/x)=2 cos θ , then x is equal to

Question

If x+(1/x)=2 cos θ , then x is equal to (A)  cos text θ +i text sin text θ  (B)  cos text θ -i text sin text θ  (C)  cos text θ ± i text sin text θ  (D) None of these

Tardigrade Admin · Accepted Answer

Given x+(1/x)=2 cos θ ⇒ x2-2x cos θ +1=0 ∴ x=(2 cos θ ± √4cos2θ -4/2) = cos θ ± (√-4(1- cos 2θ )/2) = cos θ ± (2i sin θ /2) = cos θ ± sin θ

Q. If $x + \frac{1}{x} = 2 cos θ,$ then $x$ is equal to

$cos θ + i s in θ$

$cos θ - i s in θ$

$cos θ \pm i s in θ$

None of these

Given $x + \frac{1}{x} = 2 cos θ$
$\Rightarrow$ $x^{2} - 2 x cos θ + 1 = 0$
$∴$ $x = \frac{2 c o s θ \pm 4 co s ^{2} θ - 4}{2}$
$= cos θ \pm \frac{- 4 ( 1 - c o s ^{2} θ )}{2}$
$= cos θ \pm \frac{2 i s i n θ}{2}$ $= cos θ \pm sin θ$

Q. If x+x1​=2cosθ, then x is equal to

cosθ+isinθ

cosθ−isinθ

cosθ±isinθ