How do i simplify this $\cos{\theta}=\frac{1-\sin^2{\theta}}{1+\cos{\theta}}$ I was wondering if someone could help me solve this equation: $$\cos{\theta}=\frac{1-\sin^2{\theta}}{1+\cos{\theta}}$$

$\cos{\theta}=\dfrac{1-\sin^2{\theta}}{1+\cos{\theta}}$:
1.)  Multiply through by $1 + \cos \theta$:
$\cos \theta + \cos^2 \theta = 1 - \sin^2 \theta$;
2.)  Add $\sin^2 \theta$ to each side:
$\cos \theta + \cos^2 \theta + \sin^2 \theta = 1$;
3.)  Use $\cos^2 \theta + \sin^2 \theta = 1$ on the left:
$\cos \theta + 1 = 1$;
4.)  Subtract $1$ throughout:
$\cos \theta = 0$:
5.)  Deduce from item (4) that $\theta$ must be an odd multiple of $\pi / 2$:  $\theta = (2n + 1)\pi / 2$ for $n$ an integer.
And that's it!
Hope this helps!  Cheerio,
and as always,
Fiat Lux!!!
