How do you prove $tan p + cot p = 2 csc 2 p$ ?

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Answer 1 · 2016-01-22T10:35:01

This is true $tan p+cot p=2 csc 2p$ see the explanation

the given $tan p+cot p=2 csc 2p$
start from left side
$sin p/cos p+cos p/sin p=2 csc 2p$

$sin p/cosp*sinp/sinp+cos p/sin p *cos p/cos p=2 csc 2p$

$sin^2 p/(sin p cos p)+cos^2p/(sin p cos p)=2 csc 2p$

from $sin^2p+cos^2p=1$ equation becomes
$(sin^2 p+cos^2p)/(sin p cos p)=2 csc 2p$

$1/(sin p cos p)=2 csc 2p$

$1/(sin p cos p)*2/2=2 csc 2p$
$2/(2sin p cos p)=2 csc 2p$

From $sin 2p=2 sin p cos p$ equation becomes
$2/(sin 2p)=2 csc 2p$

$2*(1/(sin 2p))=2 csc 2p$
Take note: $csc 2p=1/(sin 2p)$
$2 csc 2p=2 csc 2p$

How do you prove tan p + cot p = 2 csc 2 ptan p + cot p = 2 csc 2 p?