Question

Simplify (1+tanx)^2

The answer is (1-sinx)(1+sinx)

Here's what I do:

1 + 2tanx + tan^2x

When I simplify it becomes
1 + 2(sinx/cosx) + (1+secx)(1-secx)

What am I doing wrong?

Answer 1

(1+tanx)^2 ≠ (1-sinx)(1+sinx)

RS = 1 - sin^2 x
= cos^2 x

and cos^2 x is certainly not equal to (1+tanx)^2
try x = 45°
(1+tan45)^2 = (1+1)^2 = 4
cos^2 (45°) = (1/√2)^2 = 1/4

no wonder you got nowhere with your work.

check the question, or check your typing.