Expert: Josh - 3/2/2006

Question
tan + cos / 1 + sin = sec

Answer
Steve,

With fractions displayed on a single line, you really need to use parentheses to indicate exactly which part of the expression appears in the numerator (which part of the expression appears in the denominator).

What you have typed suggests that we have three separate terms on the left hand side (LHS) of the equation.

If this is not what the question says, for instance, if there are only two terms, adding
(i) tan(x) to
(ii) cos(x) over "1+sin(x)"
This can only be properly understood as
tan(x) + cos(x)/[1+sin(x)]

If there is only one fractional term, for instance, if the numerator reads tan(x)+cos(x), and the denominator reads 1+sin(x), you need to show this as
[tan(x)+cos(x)]/[1+sin(x)]

I can only tell you that secant(x) is the inverse of cosine(x). i.e., sec(x)=1/cos(x). To prove the identity given in the question, you may consider multiplying both sides by cos(x) and show that the resultant expression on the LHS is equivalent to 1. There might be simplier ways, but my effort is hampered by the ambiguity in your expression. (Not your fault, just that typesetting is really different to writing, where you can afford to write things on top of (or under) a fraction bar).

Please get back to me, restating the question using the suggested convention. I really want to help you with this.