Question

What is the domain of `f(x)=secx`?

Answer 1

By rewriting a bit,

`f(x)=secx=1/cosx`.

Since the denominator cannot be zero, we need to exclude numbers that make `cosx` equal to zero.

Since for all integer `n`,

`cos(pi/2+npi)=cos({2n+1}/2pi)=0`,

the domain of `f` is all real numbers except for `x={2n+1}/2pi` for all integer `n`.

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I hope that this was helpful.