Question

How do you verify the identity: `cosx cscx/cot^2x=Tanx`?

Answer 1

`cosx(cscx)/(cot^2x)`

`=cosx(1/sinx)/(cos^2x/sin^2x)`

`=cosx(sin^2x)/(sinxcos^2x)`

`=sinx/cosx`

`=tanx`

Answer 2

`"see explanation"`

Explanation:

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

`•color(white)(x)cscx=1/sinx" and "cotx=cosx/sinx`

`•color(white)(x)cotx=1/tanxhArrtanx=1/cotx`

`"consider the left side"`

`cosx xx(1/sinx)/(cot^2x)`

`=(cosx/sinx)/cot^2x`

`=cotx/cot^2x`

`=1/cotx=tanx="right side "rArr"verified"`