Solving Inequality: (1+tg(x))*cos^2(x) > 1

[Icelove]

Homework Statement

(1 + tg(x)) * cos^2(x) > 1, solve the inequality

Homework Equations

tg(x) = sin(x)/cos(x)
cos(x) * sin(x) = 1/2 sin(2x)

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

 

[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.

 

[singular]

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.

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.

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$$sin2x=2sinxcosx$$