# Math Help - How do I get the final solution?

1. ## How do I get the final solution?

Hi

Could someone please show me how to get from the LHS to the RHS???

2. Originally Posted by Sunyata
Hi

Could someone please show me how to get from the LHS to the RHS???
$\frac{atan\theta}{tan\theta-sec\theta+1}=\frac{a\frac{sin\theta}{cos\theta}}{\ frac{sin\theta}{cos\theta}-\frac{1}{cos\theta}+1}$

$=\frac{asin\theta}{sin\theta-1+cos\theta}=\frac{asin\left(\frac{2\theta}{2}\rig ht)}{sin\left(\frac{2\theta}{2}\right)+cos\left(\f rac{2\theta}{2}\right)-1}$

$=\frac{2asin\frac{\theta}{2}cos\frac{\theta}{2}}{2 sin\frac{\theta}{2}cos\frac{\theta}{2}+cos^2\left( \frac{\theta}{2}\right)-sin^2\left(\frac{\theta}{2}\right)-1}$

$=\frac{2asin\frac{\theta}{2}cos\frac{\theta}{2}}{2 sin\frac{\theta}{2}cos\frac{\theta}{2}+\left(1-sin^2\left(\frac{\theta}{2}\right)\right)-sin^2\left(\frac{\theta}{2}\right)-1}$

$=\frac{2asin\frac{\theta}{2}cos\frac{\theta}{2}}{2 sin\frac{\theta}{2}cos\frac{\theta}{2}-2sin^2\left(\frac{\theta}{2}\right)}$

$=\frac{2acos\frac{\theta}{2}}{2cos\frac{\theta}{2}-2sin\frac{\theta}{2}}$

$=\frac{acos\frac{\theta}{2}}{cos\frac{\theta}{2}-sin\frac{\theta}{2}}$