Question

How to find tan 22.5
(value is in degrees)

Answer 1

Do you know half-angle identities?

Answer 2

Or you could just use a hacky way using the sum tan(A + B).

Answer 3

Which two angles i should take

Answer 4

tan22.5=sin45/(1+cos45)
=sqrt2/(2+sqrt2)=sqrt2-1

Answer 5

Like that

Answer 6

First note that \(22.5\) is the half of \(45\). So you would have to work around with \(45^{\circ}\).\[\tan(22.5 + 22.5) = \dfrac{\tan(22.5) + \tan(22.5)}{1 - \tan(22.5)\tan(22.5)}\]\[\Rightarrow \tan(45) = \dfrac{2\tan(22.5)}{1 -\tan^2(22.5)}\]\[\Rightarrow 1 - \tan^2 (22.5) = 2\tan(22.5)\]And your method is just as legible.

Answer 7

But...

Answer 8

\[\tan^2(22.5) + 2\tan(22.5) - 1 = 0\]\[\tan(22.5) = \dfrac{-2 \pm \sqrt{4 + 4}}{2}\]It'd be the positive solution because you know why.

Answer 9

yup thank you actually i was doing quadratic i was not sure how to find tan22.5