Please simplify this trigonometric expression. (sin x)/(1 + sec x) Thanks!

Question

Basic Pre-Calculus question. Normally, I'd use Pythagorean Identities or other methods like factoring, but this one is specifically challenging. I forgot how to do this, so some help would be appreciated. Thank you!

Answer 1

IMHO, the given is about as simple as it gets, if you define simple as with the least number of symbols.

An alternativec is (sin x cos x) / (cos x + 1). And that is actually more symbols

Answer 2

Use the identity   secx = 1 / cosx

 

 

1 + secx = 1 + (1 / cosx)

 

             = (cosx + 1) / cosx

 

 

Then,

 

sinx / (1 + secx) = sinx * (cosx / (cosx + 1))

 

                        = sinxcosx / (cosx + 1)

= sin(2x) / 2(cosx + 1)