Today I was solving an exercise and while checking the solution on WolframAlpha, the website used the following identity:
\tan \left({\pi\over4}-{\alpha\over2} \right) = \sec(\alpha)-\tan(\alpha)
Since I've never seen that formula, I tried to calculate it with the identities I know, especially using
\tan \left({\pi\over4}-{\alpha\over2} \right) = {(1-\tan({\alpha\over2}))\over(1+\tan({\alpha\over2}))},
but I couldn't make it work.
Is this a known property of trigonometry, like for example \cos({\pi\over2}-x)=\sin(x)?
