Question

If `(sec(t) - 1)/(sec(t) + 1) = (A - cos(t))/(A + cos(t))`, then what does A =?

I tried solving it but I get stuck every time, can someone please help?

Answer 1

`A = 1`

Explanation:

Given:

`(sec(t) - 1)/(sec(t) + 1) = (A - cos(t))/(A + cos(t))`

Multiply the left side by 1 in the form of `cos(t)/cos(t)`:

`cos(t)/cos(t)(sec(t) - 1)/(sec(t) + 1) = (A - cos(t))/(A + cos(t))`

Distribute the cosine function over the numerator and the denominator:

`(cos(t)sec(t) - cos(t))/(cos(t)sec(t) + cos(t)) = (A - cos(t))/(A + cos(t))`

We know that `cos(t)sec(t) = 1`:

`(1 - cos(t))/(1 + cos(t)) = (A - cos(t))/(A + cos(t))`

By matching terms we observe that `A = 1`