Question

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

Answer 1

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

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`