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# Help Zone

### Student Question

Secondary V • 2mo.

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

Mathematics

## Explanations (1)

• Explanation from Alloprof

Explanation from Alloprof

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Team Alloprof • 2mo. edited May 20

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 !