Answer
$\cos x=\dfrac {1-\tan ^{2}\dfrac {x}{2}}{1+\tan ^{2}\dfrac {x}{2}}$
Work Step by Step
$\cos x=\cos ^{2}\dfrac {x}{2}-\sin ^{2}\dfrac {x}{2}=\left( \dfrac {1}{\sqrt {1+\tan ^{2}\dfrac {x}{2}}}\right) ^{2}-\left( \dfrac {\tan \dfrac {x}{2}}{\sqrt {1+\tan ^{2}\dfrac {x}{2}}}\right) ^{2}=\dfrac {1-\tan ^{2}\dfrac {x}{2}}{1+\tan ^{2}\dfrac {x}{2}}$
