Question

Question #6c1d0

Answer 1

`"see explanation"`

Explanation:

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

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

`"consider the left hand side"`

`rArr(1+cotx)/(1+tanx)`

`=(1+cosx/sinx)/(1+sinx/cosx)`

`=((sinx+cosx)/sinx)/((cosx+sinx)/cosx)`

`=cancel(sinx+cosx)/sinx xxcosx/cancel(cosx+sinx)`

`=cosx/sinx`

`=cotx=" right hand side "rArr"proven"`

Answer 2

`(1+cotx)/(1+tanx)=(1+cotx)/(1+1/cotx)=(1+cotx)/{(1+cotx)/cotx}`

`={cotxcancel((1+cotx))}/cancel((1+cotx))=cotx`.