Secondary V • 5mo.
would someone be able to explain me how to prove this with trig identities?
would someone be able to explain me how to prove this with trig identities?
Explanation from Alloprof
This Explanation was submitted by a member of the Alloprof team.
Hi !
Firstly, are the \(sec\) et \(tan\) squared ? Or is the angle in \(2x\) ?
In any case, to prove this relation, you need to work only on one side of the equation. You can try with the right side and use these identities.
$$ \tan(2x)=\dfrac{2 \tan x}{1-\tan^2x} $$
$$ \text{sec}(x)=\dfrac{1}{\cos(x)} $$
$$ \cos(2x)=\cos^2x-\sin^2 x $$
You can simplify this last identity with the Pythagorean identity.
$$ cos^2x+sin^2x=1 $$
I will let you try the prove this equation by yourself and if you have any other questions, feel free to ask them.
Have a nice day !