Question

How do you prove `(1+tanx)/(1+cotx)= secx/cscx`?

Answer 1

Please see below.

Explanation:

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

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

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

= `sinx/cosx`

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

= `secx/cscx`