Question

(1+tan^2x)/tanx ?

Answer 1

`cotx+tanx`

Explanation:

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

`•color(white)(x)cotx=1/tanx`

`rArr(1+tan^2x)/tanx`

`=1/tanx+tan^2x/tanx=cotx+tanx`

Answer 2

`cscxsecx`

Explanation:

Another method:
Use identities: `1+tan^2theta= sec^2theta`
`sec^2theta= 1/cos^2theta`
`tanx= sinx/cosx`
`1/sinx= cscx`

Start:
`(1+tan^2x)/tanx=`

`(sec^2x)/tanx=`

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

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

`(1/(sinxcosx))=`

`cscxsecx`