**Q) **Prove that sec A (1- sin A)(sec A + tan A) = 1

**Ans: **Let’s start from LHS

LHS = sec A (1- sin A)(sec A + tan A)

=

=

=

We know that sin^{2}A + cos^{2}A = 1

or we can say that, 1 – sin^{2}A = cos^{2}A

LHS =

= 1 ……….. RHS

**Hence proved!**