Respuesta :
Answer:
It is identity.
It is true for any x in the domain of the equation.
Step-by-step explanation:
Recall the Pythagorean Identity:
[tex]\sin^2(x)+\cos^2(x)=1[/tex].
Divide both sides be [tex]\cos^2(x)[/tex]:
[tex]\frac{\sin^2(x)}{\cos^2(x)}+\frac{\cos^2(x)}{\cos^2(x)}=\frac{1}{\cos^2(x)}[/tex]
[tex]\tan^2(x)+1=\sec^2(x)[/tex].
[tex]\tan^2(x)+1=\sec^2(x)[/tex] is also known as a Pythagorean Identity as well.
I'm going to apply this last identity I wrote to your equation on the left hand side.
Replacing [tex]\sec^2(x)[/tex] with [tex]\tan^2(x)+1[/tex]:
[tex]-\tan^2(x)+[\tan^2(x)+1][/tex]
Distribute:
[tex]-\tan^2(x)+\tan^2(x)+1[/tex]
Combine like terms:
[tex]0+1[/tex]
[tex]1[/tex]
This is what we also have on the right hand side so we have confirmed your given equation is an identity.
