Sec(arctan(-3/5)) is and can you provide a step by step process !

Let be some angle so that .

Recall that

The identity above gives us two possible answers, but they can't both be right: . The caveat is that and are not mutual inverse functions. While

is true, the converse is not. The function can only return values between and .

To find out which value is correct, we have to use what we know about the function. is negative only when ; over this domain, we expect to have be positive, which in turn means should be positive.

So we have