There are two questions of my homework I'm having trouble with.. I think we are supposed to show how they are true. In other words, make one side look exactly like the other one by using the identities.

Question

1. cosX/(1-sinX)=(1+sinX)/cosX

2. (secX+tanX)/(secX-tanX)=(1+2sinX+sin^(2)X)/cos^(2)X)

Please help, thanks

Answer 1

for the first, multiply the LS by (1+sinx)/(1+sinx)
It will turn into the RS

2.
LS = (1/cosx + sinx/cosx)/(1/cosx - sinx/cosx)
we have a common denominator
and remember how to divide fractions ...

= (1+sinx)/(1-sinx)

RS = (1+sinx)(1+sinx)/(1 - sin^2 x)
= (1+sinx)(1+sinx)/[(1+sinx)(1+sinx)]
= (1+sinx)/(1-sinx)
= LS

Answer 2

Thanks!