SOLUTION: if secA - cosA=3/2 then secA=?

Question 825939: if secA - cosA=3/2 then secA=?
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

When you are not sure what to do when solving these equations (or proving identities), try rewriting any sec's, csc's, tan's or cot's in terms of sin's and/or cos's. (Note: Don't start doing this automatically every time. Just do it when you see no other way.) Rewriting our equation this way we get:

Next, we'll eliminate the fractions by multiplying both sides by the lowest common denominator (LCD). The LCD of cos(A) and 2 is 2cos(A).

On the left side we must use the Distributive Property:

Each denominator cancels with some part of 2cos(A):

This is a quadratic. So we want a zero on one side as we solve it. I'm going to subtract the entire left side from both sides (since I like the squared term to have a positive coefficient):

Now we factor:

From the Zero Product Property:
or
Solving these for cos(A) we get:
or
We should recognize that a cos is never equal to -2. So there is no solution for that equation. So only
cos(A) = 1/2 is true.

Normally we would proceed to find A at this point. But the problem asks for the value of sec(A). Since sec(A) is the reciprocal of cos:

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