Respuesta :

arthurpdc
Let E the expression of the left side of the equation:

[tex]E=\sec^6(x) (\sec (x)\tan (x)) - \sec^4(x) (\sec (x)\tan (x))\\\\ E=\sec^7(x)\tan(x)-\sec^5(x)\tan(x)\\\\ E=\sec^5(x)\tan(x)(\sec^2(x)-1)[/tex]

We must know that [tex]\tan^2(x)+1=\sec^2(x)\iff \sec^2(x)-1=\tan^2(x)[/tex]. So, using in the equation above:

[tex]E=\sec^5(x)\tan(x)(\underbrace{\sec^2(x)-1}_{\tan^2(x)})\\\\ E=\sec^5(x)\tan(x)(\tan^2(x))\\\\ \boxed{E=\sec^5(x)\tan^3(x)}[/tex]

Then, the equation is true.

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