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

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

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Answer 1 · 2016-01-22T10:35:01

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

Explanation:

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

$\frac{sin p}{cos p} \cdot \frac{sin p}{sin p} + \frac{cos p}{sin p} \cdot \frac{cos p}{cos p} = 2 csc 2 p$ $sin p/cosp*sinp/sinp+cos p/sin p *cos p/cos p=2 csc 2p$

$\frac{{sin}^{2} p}{sin p cos p} + \frac{{cos}^{2} p}{sin p cos p} = 2 csc 2 p$ $sin^2 p/(sin p cos p)+cos^2p/(sin p cos p)=2 csc 2p$

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

$\frac{1}{sin p cos p} = 2 csc 2 p$ $1/(sin p cos p)=2 csc 2p$

$\frac{1}{sin p cos p} \cdot \frac{2}{2} = 2 csc 2 p$ $1/(sin p cos p)*2/2=2 csc 2p$
$\frac{2}{2 sin p cos p} = 2 csc 2 p$ $2/(2sin p cos p)=2 csc 2p$

From $sin 2 p = 2 sin p cos p$ $sin 2p=2 sin p cos p$ equation becomes
$\frac{2}{sin 2 p} = 2 csc 2 p$ $2/(sin 2p)=2 csc 2p$

$2 \cdot (\frac{1}{sin 2 p}) = 2 csc 2 p$ $2*(1/(sin 2p))=2 csc 2p$
Take note: $csc 2 p = \frac{1}{sin 2 p}$ $csc 2p=1/(sin 2p)$
$2 csc 2 p = 2 csc 2 p$ $2 csc 2p=2 csc 2p$

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

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How do you prove tan p + cot p = 2 csc 2 ptanp+cotp=2csc2ptan p + cot p = 2 csc 2 p?

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Explanation:

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