If $\left(\frac{\cos \theta+i \sin \theta}{\sin \theta+i \cos \theta}\right)^{2020}+\left(\frac{1+\cos \theta+i \sin \theta}{1-\cos \theta+i \sin \theta}\right)^{2021} = x+i y$,then the value of $x+y$ at $\theta=\frac{\pi}{2}$ is
- A$2$
- B$1$
- C$-1$
- D$2020$
Explore More
Similar Questions
If $x_r = \cos(\pi/3^r) - i\sin(\pi/3^r)$ (where $i = \sqrt{-1}$),then the value of $x_1 \cdot x_2 \cdot x_3 \cdots \infty$ is:
Let $z$ be a complex number (not lying on the $X$-axis) of maximum modulus such that $\left| z + \frac{1}{z} \right| = 1$. Then:
Difficult
View SolutionIf $x+iy = \frac{3}{2+\cos \theta + i \sin \theta}$,then $x^2+y^2 =$
If $\frac{1-10 i \cos \theta}{1-10 \sqrt{3} i \sin \theta}$ is purely real,then one of the values of $\theta$ is
The sum of all possible values of $\theta \in[-\pi, 2 \pi]$, for which $\frac{1+i \cos \theta}{1-2 i \cos \theta}$ is purely imaginary, is equal to (in $\pi$)
DifficultJEE MAIN 2024
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo