WBJEE · Maths · Complex Number
If \(x+\frac{1}{x}=2 \cos \theta\), then for any integer \(n, x^n+\frac{1}{x^n}=\)
- A \(2 \cos n \theta\)
- B \(2 \sin n \theta\)
- C \(2 i \cos n \theta\)
- D \(2 i \sin n \theta\)
Answer & Solution
Correct Answer
(A) \(2 \cos n \theta\)
Step-by-step Solution
Detailed explanation
Hints: \(x+\frac{1}{x}=2 \cos \theta\) Let \(x=\cos \theta+1 \sin \theta\) \(\frac{1}{x}=\cos \theta-1 \sin \theta\) Thus \(x^n+\frac{1}{x^n}=2 \cos n \theta\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The quadratic equation whose roots are three times the roots of \(3 a x^2+3 b x+c=0\) isWBJEE 2009 Medium
- Given \(f(x)=e^{\sin x}+e^{\cos x}\). The global maximum value of \(f(x)\)WBJEE 2023 Medium
- The number of points at which the function \(f(x)=\max \{a-x, a+x, b\},-\infty < x < \infty\) \(0 < a < b\) cannot be differentiable, isWBJEE 2016 Medium
- The locus of the point of intersection of the straight lines \(\frac{x}{a}+\frac{y}{b}=K\) and \(\frac{x}{a}-\frac{y}{b}=\frac{1}{K}\),
where \(K\) is a non-zero real variable, is given byWBJEE 2016 Medium - If \(\left(\frac{3}{2}+i \frac{\sqrt{3}}{2}\right)^{50}=3^{25}(x+i y)\) where \(x\) and \(y\)
are real, then the ordered pair \((x, y)\) isWBJEE 2012 Medium - Let \(a, b, c, p, q\) and \(r\) be positive real numbers such that \(a, b\) and \(c\) are in GP and \(a^{p}=b^{q}=c^{r}\). Then,WBJEE 2012 Medium
More PYQs from WBJEE
- If the four points with position vectors \(-2\hat i+\hat j + \hat k, \hat i+\hat j+\hat k,\hat j- \hat k\) and \(\lambda \hat j + \hat k\) are coplanar, then \(\lambda\) is equal toWBJEE 2015 Easy
- Eleven apples are distributed among a girl and a boy, Then, which one of the following statements is true?WBJEE 2013 Medium
- Let \(f(x)=\left\{\begin{array}{ll}\int_{0}^{x}|1-t| d t, & x>0 \\ x-\frac{1}{2}, & x \leq 1\end{array} .\right.\) ThenWBJEE 2014 Medium
- A ball falls from a height \(h\) upon a fixed horizontal floor. The co-efficient of restitution for the collision between the ball and the floor is 'e'. The total distance covered by the ball before coming to rest is [neglect the air resistance]WBJEE 2025 Medium
- The number of unpaired electrons in the uranium \(\left({ }_{92} \mathrm{U}\right)\) atom is:WBJEE 2020 Easy
- Suppose that the equation \(f(x)=x^{2}+b x+c=0\) has two distinct real roots \(\alpha\) and \(\beta\). The angle between the tangent to the curve \(y=f(x)\) at the point \(\left(\frac{\alpha+\beta}{2}, f\left(\frac{\alpha+\beta}{2}\right)\right)\) and the positive direction of the \(x\) -axis isWBJEE 2014 Hard