simplying an expression

[tsh44]

Hi I need to simplify this expression and I would just like someone to confirm my work and see of i did the problem correctly. Thanks.

The expression is:

[(1+tan^2x) (1-cos2x)]/ 2

I then changed the cos 2x so I got this:

[(1+tan^2x) (1-(1-2Sin^2x)] / 2

Then:

[(1+tan^2x) (-2Sin^2X)] /2

Then I changed the (1+tan^2x) to sec^2x so :

[(sec^2x) (-2Sin^2x)] /2

and for a final answer I got -sec^2xsin^2x

Thanks for any help

 

[galactus]

\(\displaystyle \frac{(1+tan^{2}(x))(1-cos(2x))}{2}\)

=\(\displaystyle \frac{(sec^{2})(1-(1-2sin^{2}(x)))}{2}\)

=\(\displaystyle \frac{(sec^{2}(x))(2sin^{2}(x))}{2}\)

=\(\displaystyle \frac{2sin^{2}(x)}{2cos^{2}(x)}\)

=\(\displaystyle tan^{2}(x)\)