Show that :cos4θ-sin4θ+1=2cos2θ
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< div class="emoji emoji_robot" > < div class="emoji__siren" > < /div > < div class="emoji__face" > < div class="emoji__connector" > < /div > < div class="emoji__eyes" > < div class="emoji__eye" > < /div > < div class="emoji__eye" > < /div > < /div > < div class="emoji__nose" > < /div > < div class="emoji__mouth" > < /div > < /div > < /div > < style > :root { --color-white: #fff; --color-dark: #4b4241; --color-bg: #fffcee; --tooth-pos: 6px; } * { padding: 0; margin: 0; box-sizing: border-box; } body { height: 100vh; width: 100vw; padding: 30px; display: grid; place-items: center; background-color: var(--white); } .emoji { width: 106px; height: 106px; position: relative; border: 1px solid rgba(255, 255, 255, 0); border-radius: 26%; box-shadow: inset -8px -7px 0px rgba(0, 0, 0, 0.05); } .emoji_robot { background: #54cae2; background: linear-gradient(180deg, #6ed0e4 0%, #4abbe3 50%, #4ec2e5 100%); } .emoji_robot .emoji__siren { position: absolute; top: -4px; left: 50%; border-radius: 3px; width: 18px; height: 10px; background-color: var(--color-dark); margin-left: -9px; }.emoji_robot .emoji__siren::before { content: ''; position: absolute; top: -7px; width: 14px; height: 7px; background: #f9dc2e; background: radial-gradient(circle, #f9dc2e 0%, #f9a02e 100%); margin-left: -7px; left: 50%; border-top-left-radius: 6px; border-top-right-radius: 6px; animation: flasher 0.5s ease-in-out infinite; } @keyframes flasher { 0% { transform: scale(1.2); } 50% { transform: scale(1); } 100% { transform: scale(1.2); } } ..emoji_robot .emoji__face { width: 100%; height: 100%; overflow: hidden; position: relative; margin-top: -1px; } .emoji_robot .emoji__connector { width: 26px; height: 20px; border-radius: 50%; top: -9px; position: absolute; background-color: var(--color-dark); left: 52px; margin-left: -13px; z-index: 10; } .emoji_robot .emoji__eyes { position: relative; display: flex; justify-content: space-between; top: 24px; width: 58px; margin: 0 auto; } .emoji_robot .emoji__eye { position: relative; display: flex; align-items: center; justify-content: center; background-color: var(--color-white); width: 28px; height: 28px; border-radius: 50%; } .emoji_robot .emoji__eye:after { content: ''; width: 12px; height: 12px; background-color: var(--color-dark); border-radius: 50%; animation: eye-anima 0.5s ease infinite;} @keyframes eye-anima { 0% { transform: scale(1.2); } 50% { transform: scale(1); } 100% { transform: scale(1.2); } } .emoji_robot .emoji__mouth { width: 60px; margin: 0 auto; height: 18px; background: repeating-linear-gradient(90deg, var(--color-dark), var(--color-dark) 3px, #fff 3px, #fff 15px), var(--color-dark); background-position: 6px; border-radius: 8px; top: 38px; position: relative; animation: tooth-pos 13s linear infinite; } @keyframes tooth-pos { to { background-position: 200px; } } .emoji_robot .emoji__nose { position: absolute; top: 50%; left: 50%; margin-top: 2px; margin-left: -2px; background-color: var(--color-dark); transform: rotate(60deg) skewX(-30deg) scale(1, 0.866); } .emoji_robot .emoji__nose, .emoji_robot .emoji__nose::before, .emoji_robot .emoji__nose::after { width: 7px; height: 7px; border-top-right-radius: 60%; } .emoji_robot .emoji__nose::before, .emoji_robot .emoji__nose::after { content: ''; position: absolute; background-color: inherit; } .emoji_robot .emoji__nose::before { transform: rotate(-135deg) skewX(-45deg) scale(1.414, 0.707) translate(0, -50%); } .emoji_robot .emoji__nose::after { transform: rotate(135deg) skewY(-45deg) scale(0.707, 1.414) translate(50%); } < /style >