# Trig algebra

1. Dec 8, 2009

### Icelove

1. The problem statement, all variables and given/known data
(1 + tg(x)) * cos^2(x) > 1, solve the inequality

2. Relevant equations
tg(x) = sin(x)/cos(x)
cos(x) * sin(x) = 1/2 sin(2x)

3. The attempt at a solution
I got my final value of:
1-sin^2(x) + 1/2 sin(2x) > 1
but because of the 2 inside the sin
I'm kinda lost so I can't use quadratic formula I presume

2. Dec 8, 2009

### grief

Let me rearrange that a little for you:

1/2sin(2x)>sin^2(x)

which is actually nicer in the following form:

sin(x)cos(x)>sin^2(x).

This should be easier to solve.

3. Dec 8, 2009

### singular

It is important for you to realize where this came from.
If you have notes, cheat sheet, book, or webpage with trig identities, look at the double angle identities.

$$sin2x=2sinxcosx$$