Question

Question #5abd9

Answer 1

The right side of the equation was missing a minus sign between the `cotx` and `tanx`.

Explanation:

`(1-2(sinx)^2)/((sinx)(cosx))`

`=1/((sinx)(cosx))-(2(sinx)^2)/((sinx)(cosx))`

`=((sinx)^2+(cosx)^2)/((sinx)(cosx))-2tanx`

`=((sinx)^2/((sinx)(cosx)))+((cosx)^2/((sinx)(cosx)))-2tanx`

`=((sinx)/(cosx))+((cosx)/(sinx))-2tanx`

`=tanx+cotx-2tanx`

`=cotx-tanx`

Answer 2

`LHS=(1-2sin^2x)/(sinxcosx)`

`=(cos^2x+sin^2x-2sin^2x)/(sinxcosx)`

`=(cos^2x-sin^2x)/(sinxcosx)`

`=cos^2x/(sinxcosx)-sin^2x/(sinxcosx)`

`=cosx/sinx-sinx/cosx`

`=cotx-tanx`