I taught three basic trigonometric identities. One of my 9th grade students asked: how can we say $$\sec^2x-\tan^2x=1$$ is an identity since when we plug in $x=\frac{\pi}{2}$ the identity fails which creates an ambiguity for the definition of an identity in mathematics.

How should I try to explain him without entering into calculus part?

I taught three basic trigonometric identities. One of my 9th grade students asked: How can we say $$\sec^2x-\tan^2x=1$$ is an identity since when we plug in $x=\frac{\pi}{2}$ the identity fails which creates an ambiguity for the definition of an identity in mathematics?

How should I try to explain him without entering into calculus part?

I taught three basic trigonometric identities. One of my 9th grade student asked how can we say $$\sec^2x-\tan^2x=1$$ is an identity since when we plug in $x=\frac{\pi}{2}$ the identity fails which creates an ambiguity for the definition of an identity in mathematics.

How should I try to explain him without entering into calculus part?

I taught three basic trigonometric identities. One of my 9th grade students asked: how can we say $$\sec^2x-\tan^2x=1$$ is an identity since when we plug in $x=\frac{\pi}{2}$ the identity fails which creates an ambiguity for the definition of an identity in mathematics.

How should I try to explain him without entering into calculus part?

I taught three basic trigonometric identities. One of my 9th grade student asked how can we say $$sec^2x-tan^2x=1$$ is an Identity since when we plug in $x=\frac{\pi}{2}$ the identity fails which creates an ambiguity for the definition of an identity in Mathematics.

How should i try to explain him without entering into calculus part..

I taught three basic trigonometric identities. One of my 9th grade student asked how can we say $$\sec^2x-\tan^2x=1$$ is an identity since when we plug in $x=\frac{\pi}{2}$ the identity fails which creates an ambiguity for the definition of an identity in mathematics.

How should I try to explain him without entering into calculus part?