Prove the following:

Question

[1+sinx]/[1+cscx]=tanx/secx
=[1+sinx]/[1+1/sinx]
=[1+sinx]/[(sinx+1)/sinx]
=[1+sinx]*[sinx/(sinx+1)]
=[sinx+sin^2x]/[sinx+1]
=[sinx+(1-cos^2x)]/[sinx+1]
=???

This is where I'm stuck. Can someone help me. Please check what I got is right so far it's possible that I made a mistake somewhere.

Please and Thank you

Answer 1

LS = (1 + sinx)/(1 + 1/sinx)
= (1 + sinx)/( ( sinx + 1)/sinx )
= (1 + sinx) ( sinx/(1+sinx))
= sinx

RS = (sinx/cosx)(cosx)
= sinx
= LS

Answer 2

so I have to do both sides but I thought can only do one side

Answer 3

2x