achristman
achristman
03-02-2017
Mathematics
contestada
is this an identity?
1+sec^2x=tan^2x
Respuesta :
arthurpdc
arthurpdc
12-02-2017
No, the correct identity is [tex]\tan^2(x)+1=\sec^2(x)[/tex]. It is obtained by dividing the both sides of the Pythagorean Trigonometric Identity by cos²(x):
[tex]\sin^2(x)+\cos^2(x)=1\\\\ \dfrac{\sin^2(x)+\cos^2(x)}{\cos^2(x)}=\dfrac{1}{\cos^2(x)}\\\\ \dfrac{\sin^2(x)}{\cos^2(x)}+\dfrac{\cos^2(x)}{\cos^2(x)}=\dfrac{1}{\cos^2(x)}\\\\ \boxed{\tan^2(x)+1=\sec^2(x)}~~\blacksquare[/tex]
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