Someone can explain me why $tan(-\frac{\pi}4+\arctan x)=\frac{x-1}{x+1}$??
I try to understand it, bot I don't understand how to came from one side to the other...
Thank you!
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.
Sign up to join this communitySomeone can explain me why $tan(-\frac{\pi}4+\arctan x)=\frac{x-1}{x+1}$??
I try to understand it, bot I don't understand how to came from one side to the other...
Thank you!
We know that $$\tan(a-b)=\dfrac{\tan a-\tan b}{1+\tan a\tan b}$$ So, let $b=\pi/4,a=\arctan x$. Then, $$\tan(\arctan x-\pi/4)=\dfrac{\tan \arctan x-\tan \pi/4}{1+\tan \arctan x\tan \pi/4}=\dfrac{x-1}{1+x}$$