If $2 \cos \theta=x+\frac{1}{x}$ and $2 \cos \phi=y+\frac{1}{y}$, then

$\frac{x}{y}+\frac{y}{x}=2 \cos (\theta+\phi)$

$\frac{x^m}{y^n}+\frac{y^n}{x^m}=2 \cos (m \theta+n \phi)$

$x y+\frac{1}{x y}=2 \cos (\theta-\phi)$

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Hard

1 of 1

Application +4 | -1

2 \cos \theta=x+\frac{1}{x}

and

2 \cos \phi=y+\frac{1}{y}

, then

View answer and explanation

Correct option: B

x^m y^n+\frac{1}{x^m y^n}=2 \cos (m \theta+n \phi)

Option B (

x^m y^n+\frac{{1}}{{x^m y^n}}=2 \cos (m \theta+n \phi)

) is correct because it follows from De Moivre's theorem.

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