If left(frac{cos theta+i sin theta}{sin theta | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given $	heta = \frac{\pi}{2}$,we have $\cos \frac{\pi}{2} = 0$ and $\sin \frac{\pi}{2} = 1$. Substituting these values into the first term: $\lef

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(C) Given $	heta = \frac{\pi}{2}$,we have $\cos \frac{\pi}{2} = 0$ and $\sin \frac{\pi}{2} = 1$. Substituting these values into the first term: $\left(\frac{0+i(1)}{1+i(0)}ight)^{2024} = (i)^{2024} = (i^4)^{506} = 1^{506} = 1$. For the second term: $\frac{1+\cos 	heta+i \sin 	heta}{1-\cos 	heta+i \sin 	heta} = \frac{1+0+i(1)}{1-0+i(1)} = \frac{1+i}{1+i} = 1$. Thus,the expression becomes $1^{2024} + 1^{2025} = 1 + 1 = 2$. Since $x+iy = 2$,we have $x=2$ and $y=0$. Therefore,$x+y = 2+0 = 2$.

If $\left(\frac{\cos \theta+i \sin \theta}{\sin \theta+i \cos \theta}\right)^{2024}+\left(\frac{1+\cos \theta+i \sin \theta}{1-\cos \theta+i \sin \theta}\right)^{2025}=x+i y$,then the value of $x+y$ at $\theta=\frac{\pi}{2}$ is

Similar Questions

The set of all values of $\theta$ such that $\frac{1-i \cos \theta}{1+2 i \sin \theta}$ is purely imaginary is

Let $z \in \mathbb{C}$ be such that $\frac{z^2+3i}{z-2+i}=2+3i$. Then the sum of all possible values of $z^2$ is

If $(x-iy)^{\frac{1}{3}} = a+ib$,then $\frac{ax-by}{a-b} = $

If $a, b, c$ and $d \in \mathbb{R}$ such that $a^2+b^2=4$ and $c^2+d^2=2$ and if $(a+ib)^2=(c+id)^2(x+iy)$,then $x^2+y^2$ is equal to

If the set $R = \{(a, b) : a + 5b = 42, a, b \in N\}$ has $m$ elements and $\sum_{n=1}^m (1 - i^{n!}) = x + iy$,where $i = \sqrt{-1}$,then the value of $m + x + y$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module