Math, asked by msd7chinnathala, 9 months ago

prove that
$\tan(\pi \div 4 + x ) \div \tan(\pi \div 4 - x) = (1 + \tan(x) \div 1 - \tan(x) ) {?}^{2}$

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Answered by Anonymous

$<!DOCTYPE html><html lang="en"><head><title>CUBE</title></head><body><div class="container"><div id="cube"><div class="front">Itz tua</div><div class="back">2</div><div class="right">3</div><div class="left">4</div><div class="top">Itz tua</div><div class="bottom">6</div></div></div><style>body {padding-left: 30%;padding-top: 5%;}.container {width: 200px;height: 200px;position: relative;-webkit-perspective: 1000px;-moz-perspective: 1000px;}#cube {width: 100%;height: 100%;position: absolute;-webkit-transform-style: preserve-3d;-webkit-animation: rotatecube 10s infinite;-moz-transform-style: preserve-3d;-moz-animation: rotatecube 10s infinite;}#cube div {width: 200px;height: 200px;display: block;position: absolute;border: none;line-height: 200px;text-align: center;font-size: 50px;font-weight: bold;}@-webkit-keyframes rotatecube {0% { -webkit-transform: rotateX(0deg) rotateY(360deg) rotateZ(90deg); }25% { -webkit-transform: rotateX(90deg) rotateY(270deg) rotateZ(180deg); }50% { -webkit-transform: rotateX(180deg) rotateY(180deg) rotateZ(0deg); }75% { -webkit-transform: rotateX(270deg) rotateY(90deg) rotateZ(360deg); }100% { -webkit-transform: rotateX(360deg) rotateY(0deg) rotateZ(270deg); }}@-moz-keyframes rotatecube {0% { -moz-transform: rotateX(0deg) rotateY(360deg) rotateZ(90deg); }25% { -moz-transform: rotateX(90deg) rotateY(270deg) rotateZ(180deg); }50% { -moz-transform: rotateX(180deg) rotateY(180deg) rotateZ(0deg); }75% { -moz-transform: rotateX(270deg) rotateY(90deg) rotateZ(360deg); }100% { -moz-transform: rotateX(360deg) rotateY(0deg) rotateZ(270deg); }}.front {background: rgba(255,0,0,.5);}.back {background: rgba(0,255,0,.5);}.right {background: rgba(0,0,255,.5);}.left {background: rgba(0,255,255,.5);}.top {background: rgba(255,0,255,.5);}.bottom {background: rgba(255,255,0,.5);}#cube .front {-webkit-transform: rotateY(0deg ) translateZ( 100px );-moz-transform: rotateY( 0deg ) translateZ( 100px );}#cube .back {-webkit-transform: rotateX( 180deg ) translateZ( 100px );-moz-transform: rotateX( 180deg ) translateZ( 100px );}#cube .right {-webkit-transform: rotateY( 90deg ) translateZ( 100px );-moz-transform: rotateY( 90deg ) translateZ( 100px );}#cube .left {-webkit-transform: rotateY( -90deg ) translateZ( 100px );-moz-transform: rotateY( -90deg ) translateZ( 100px );}#cube .top {-webkit-transform: rotateX( 90deg ) translateZ( 100px );-moz-transform: rotateX( 90deg ) translateZ( 100px );}#cube .bottom {-webkit-transform: rotateX( -90deg ) translateZ( 100px );-moz-transform: rotateX( -90deg ) translateZ( 100px );}</style></body></html>$

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prove that
$\tan(\pi \div 4 + x ) \div \tan(\pi \div 4 - x) = (1 + \tan(x) \div 1 - \tan(x) ) {?}^{2}$