Question

Prove that: `((1+tanx)/sinx)+((1+cotx)/cosx)=2(secx+cosecx)`?

using trigonometric identities

Answer 1

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

`=1/sinx+cancelsinx/(cosxcancelsinx)+1/cosx+cancelcosx/(sinxcancelcosx)`

`=cscx+secx+secx+cscx`

`=2(secx+cscx)=RHS`