Question regarding Trig in terms of T (1 Viewer)

[mtmccormick]

This is the Q. "Write an expression for sin 2θ in terms of t where t=tan θ/2". please explain

 

[iJimmy]

is this under 2unit couurse or 3?

 

[mtmccormick]

3 i believe

 

[andybandy]

<a href="http://www.codecogs.com/eqnedit.php?latex=\sin&space;2\theta&space;=&space;2\sin&space;\theta&space;\cos&space;\theta&space;\textup{&space;where&space;}&space;\sin&space;\theta&space;=&space;\frac{2t}{1&plus;t^{2}}&space;\textup{&space;and&space;}&space;\cos&space;\theta&space;=&space;\frac{1-t^{2}}{1&plus;t^{2}}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\sin&space;2\theta&space;=&space;2\sin&space;\theta&space;\cos&space;\theta&space;\textup{&space;where&space;}&space;\sin&space;\theta&space;=&space;\frac{2t}{1&plus;t^{2}}&space;\textup{&space;and&space;}&space;\cos&space;\theta&space;=&space;\frac{1-t^{2}}{1&plus;t^{2}}" title="\sin 2\theta = 2\sin \theta \cos \theta \textup{ where } \sin \theta = \frac{2t}{1+t^{2}} \textup{ and } \cos \theta = \frac{1-t^{2}}{1+t^{2}}" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex=2&space;\times&space;\frac{2t}{1&plus;t^{2}}&space;\times&space;\frac{1-t^{2}}{1&plus;t^{2}}&space;=&space;\frac{4t(1-t^{2})}{(1&plus;t^{2})^{2}}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?2&space;\times&space;\frac{2t}{1&plus;t^{2}}&space;\times&space;\frac{1-t^{2}}{1&plus;t^{2}}&space;=&space;\frac{4t(1-t^{2})}{(1&plus;t^{2})^{2}}" title="2 \times \frac{2t}{1+t^{2}} \times \frac{1-t^{2}}{1+t^{2}} = \frac{4t(1-t^{2})}{(1+t^{2})^{2}}" /></a>