Secondary V • 4mo.

would someone be able to explain me how to prove this with trig identities?

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Secondary V • 4mo.

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 !