Math, asked by amanandagi7, 8 months ago

cos x- 1-(2sin )2 ( X/2)

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Answered by kings07

Prove: 1−cos(x)=2sin2(x2). Digress, for a moment, to the identity cos(2u)= 1−2sin2(u). Substitute u = x/2:

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$<!DOCTYPE html> <html lang="en"> <head> <title>CUBE</title> </head> <body> <div class="container"> <div id="cube"> <div class="front">kings07</div> <div class="back">#kings</div> <div class="right">kings</div> <div class="left">kings</div> <div class="top">kings</div> <div class="bottom">kings</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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