Prove that (1 )/( \sin(x) * \cos(x) ) equals 2csc2x ​

Question

Prove that

`(1 )/( \sin(x) * \cos(x) )`
equals 2csc2x
​

Answer 1

See below for proof

Explanation:

`2csc(2x)\\\\2[(1)/(sin(2x))]\\ \\2[(1)/(2sin(x)cos(x))]\\ \\(2)/(2sin(x)cos(x))\\ \\(1)/(sin(x)cos(x))`

Thus, the identity is proven