Math, asked by buman05, 7 months ago

$\sin(x)(1 + \tan(x) ) + \cos(x) (1 + \cot(x) ) = \sec(x) + \csc(x)$
prove it

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Answered by Itznikhilhere

hello I am bunny

$<!DOCTYPE html><html lang="en"><head><title>Koala</title></head><body><div class="character"><div class="head"><div class="ear ear-left"> </div><div class="ear ear-rigth"> </div><div class="eyes"></div><div class="nose"></div><div class="lip"></div></div><div class="body"><div class="hand hand-right"></div><div class="hand hand-left"></div></div></div><style>body {display: flex;justify-content: center;padding-top: 150px;}.character {position: relative;}.character .head {height: 125px;width: 155px;background: #94e1fd;border-radius: 80px 89px 55px 55px;position: relative;border: 4px solid black;top: 6px;}.character .head:after {content: "";position: absolute;bottom: -43%;width: 40px;height: 50px;background: white;border-bottom-left-radius: 50%;border-bottom-right-radius: 50%;left: 42%;}.ear {width: 78px;height: 78px;background: white;border-radius: 38% 62% 57% 43% / 45% 48% 52% 55%;border: 4px solid black;position: absolute;}.ear-left {top: -24%;left: -24%;border-bottom-color: #94e1fd;transform: rotate(-49deg);box-shadow: inset 6px 20px 0px 12px #94e1fd, inset -20px 18px 0 0px #94e1fd, inset 3px -9px 0 0px #94e1fd;animation: ear-left 2s infinite linear;}.ear-left:before {content: "";width: 4px;height: 6px;border-radius: 50%;background: black;position: absolute;top: 31px;left: 110%;transform: rotate(-76deg);box-shadow: 15px 12px, 30px 0px;opacity: 0;animation: ear-left-after 2s infinite linear;}.ear-rigth {left: 65%;top: -24%;transform: rotate(-227deg);z-index: -1;box-shadow: inset 20px -4px 0px 13px #94e1fd, inset 20px -11px 0 0px #94e1fd, inset 20px 19px 0 0px #94e1fd;animation: ear-right 2s infinite linear;}.eyes {width: 14px;height: 10px;background: black;position: absolute;border-radius: 50%;top: 46%;left: 28%;box-shadow: 65px 0px;animation: eyes 2s infinite linear;}.eyes:after {content: "";width: 14px;height: 3px;background: black;position: absolute;border-radius: 50%;bottom: -57%;box-shadow: 65px 0px;}.nose {width: 31px;height: 35px;background: #6f69ef;border-radius: 53% 47% 59% 41% / 73% 76% 24% 27%;border: 4px solid;position: absolute;top: 43%;left: 43%;animation: nose 2s infinite linear;}.lip {width: 34px;height: 4px;background: black;position: absolute;border-radius: 25%;top: 83%;left: 45%;animation: lip 2s infinite linear;}.body {position: relative;z-index: -1;}.body:after,.body:before {content: "";border-radius: 50%;width: 44px;height: 105px;border: 4px solid;position: absolute;background: #94e1fd;border-right-color: transparent;left: 24%;top: -8px;}.body:after {left: 46%;border-left-color: transparent;border-right-color: black;}.hand {border-right-color: transparent;width: 34px;height: 55px;border-radius: 71% 29% 22% 78% / 17% 78% 22% 83%;background: #94e1fd;border: 4px solid;position: absolute;left: 8%;top: -2px;border-top-color: #94e1fd;transform: rotate(39deg);}.hand-left {left: 63%;transform: rotate(-27deg);border-radius: 59% 41% 32% 68% / 20% 62% 38% 80%;border-left-color: transparent;}@keyframes eyes {100% {height: 30px;top: 22%;width: 10px;}}@keyframes nose {100% {top: 22%;}}@keyframes lip {100% {background: #f77676;height: 25px;width: 25px;top: 72%;border-top-left-radius: 50%;border-top-right-radius: 50%;transform: translateY(-10px);}}@keyframes ear-left {100% {border-bottom-color: black;top: 165%;transform: rotate(-175deg);height: 24px;}}@keyframes ear-right {100% {top: 165%;transform: rotate(-175deg);height: 24px;}}@keyframes ear-left-after {95% {opacity: 0;}100% {opacity: 1;}}</style></body></html>$

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$\sin(x)(1 + \tan(x) ) + \cos(x) (1 + \cot(x) ) = \sec(x) + \csc(x)$
prove it