Question

How do you verify `(1+tanx)/(sinx)=cscx+secx`?

Answer 1

Use the following rules :
`tanx=sinx/cosx`
`1/sinx=cscx`
`1/cosx=secx`

Explanation:

Start from the Left hand side`("LHS")` :

`=>"LHS"=(1+tanx)/sinx=1/sinx+tanx/sinx`
`=cscx+tanx xx1/sinx=cscx+cancel(sinx)/cosx xx1/cancel(sinx)=cscx+1/cosx=color(blue)(cscx+secx)`

`QED`