Question

How to solve this identity? Thank you!

You need to prove that `cotx - coty = (sin(y-x))/(sinx * siny)`

Thank you very much!

Answer 1

`"see explanation"`

Explanation:

`"using the "color(blue)"trigonometric identities"`

`•color(white)(x)sin(y-x)=sinycosx-cosysinx`

`•color(white)(x)cotx=cosx/sinx`

`"consider the left side"`

`cotx-coty`

`=cosx/sinx-cosy/siny`

`=(cosxsiny-sinxcosy)/(sinxsiny)`

`=(sin(y-x))/(sinxsiny)`

`=" right side "rArr" verified"`