If x+1/x=2 cos θ , then for any integer n, x^n+1/(x^n)=

Correct answer: (A) 2 cos n θ. Hints: x+1/x=2 cos θ Let x=cos θ+1 sin θ 1/x=cos θ-1 sin θ Thus x^n+1/(x^n)=2 cos n θ

Q95 / 160 · WBJEE 2011 · Mathematics

If \(x+\frac{1}{x}=2 \cos \theta\), then for any integer \(n, x^n+\frac{1}{x^n}=\)

Correct answer
A
\(2 \cos n \theta\)
B
\(2 \sin n \theta\)
C
\(2 i \cos n \theta\)
D
\(2 i \sin n \theta\)

Solution

Hints: \(x+\frac{1}{x}=2 \cos \theta\) Let \(x=\cos \theta+1 \sin \theta\) \(\frac{1}{x}=\cos \theta-1 \sin \theta\) Thus \(x^n+\frac{1}{x^n}=2 \cos n \theta\)

Hence, the correct answer is option: 'A'.

Relevant Questions

If , is the root of the equation then the value of is2024Polar and Euler Form
The general value of the real angle , which satisfies the equation. is given by, (assuming is an integer)2019Polar and Euler Form
The polar coordinate of a point is The polar coordinate of the point which is such that line joining is bisected perpendicularly by the init2019Polar and Euler Form
Let and be the roots of If be a positive integer, then is2017Polar and Euler Form
If then for any integer2016Polar and Euler Form
Let be a fixed point on the circle of radius 1 centred at the origin in the argand plane and Consider an equilateral triangle inscribed in t2014Polar and Euler Form