Chemistry, asked by TheMahakals, 8 months ago

Prove the following using complex numbers.

$\displaystyle \frac{\sin((2n+1)\theta)}{(2n+1)\sin(\theta)} = \prod_{r=1}^n \left( 1-\frac{\sin^2(\theta)}{\sin^2\left(\frac{r\pi}{(2n+1)}\right)}$

Answers

Answered by BRAINLYADDICTOR

$\displaystyle \frac{\sin((2n+1)\theta)}{(2n+1)\sin(\theta)} = \prod_{r=1}^n \left( 1-\frac{\sin^2(\theta)}{\sin^2\left(\frac{r\pi}{(2n+1)}\right)}$

$<marquee behaviour-move><h1>ANSWER:</ ht></marquee>$

FOLLOW ME AND THANK MY ANSWERS

$<html><head><style>h1{text-transform:uppercase;margin-top:90px;text-align:center;font-family:Courier new,monospace;border:3px solid rgb(60,45,8);border-top:none;width:67%;letter-spacing:-6px;box-sizing:border-box;padding-right:5px;border-radius:6px;font-size:35px;font-weight:bold;}h1 span{position:relative;display:inline-block;margin-right:3px;}@keyframes shahir{0%{transform: translateY(0px) rotate(0deg);}40%{transform: translateY(0px) rotate(0deg);}50%{transform: translateY(-50px)rotate(180deg);;}60%{transform: translateY(0px)rotate(360deg);;}100%{transform: translate(0px)rotate(360deg);;}}h1 span{animation: shahir 3s alternate infinite linear;}h1 span:nth-child(1){color:red;animation-delay: 0s;}h1 span:nth-child(2){color:lightmaroon;animation-delay: 0.2s;}h1 span:nth-child(3){color:orange;animation-delay:0s;}h1 span:nth-child(4){color:pink;animation-delay: 0.4s;}h1 span:nth-child(5){color:lime;animation-delay: 0.5s;}h1 span:nth-child(6){color:purple;animation-delay: 0.3s;}h1 span:nth-child(7){color:blue;animation-delay: 0.4s;}h1 span:nth-child(8){color:yellow;animation-delay: 0.5s;} </style><meta name="viewport" content="width=device-width" ></head><body><center><div><h1>ADDIC TO R</h1></div></center></body></html>$ $<svg class= "heart" viewBox= "-2 -2 98.6 90.81"><title>Corazon</title><path stroke= "firebrick" stroke-width="3" d="M86.81,8.15a27.79,27.79,0,0,1,0,39.33L47.48,86.81,8.15,47.48A27.81,27.81,0,0,1,47.48,8.15,27.79,27.79,0,0,1,86.81,8.15Z"/></svg><style>body {display: grid;min-height: 100vh;justify-content: center;align-content: center;background: repeating-linear-gradient(circle,cyan,pink, lime);background: repeating-radial-gradient(circle, cyan,pink, lime);}@keyframes heart-path {99% {stroke-dashoffset: 0;fill: none;}100% {fill: firebrick;}}</style>$

Attachments:

Answered by Theopekaaleader

the correct answer I will be

Previous Question

Next Question

Prove the following using complex numbers. ​

Answers

Prove the following using complex numbers.

$\displaystyle \frac{\sin((2n+1)\theta)}{(2n+1)\sin(\theta)} = \prod_{r=1}^n \left( 1-\frac{\sin^2(\theta)}{\sin^2\left(\frac{r\pi}{(2n+1)}\right)}$