Expert: Sherman D. - 2/24/2008

Question
[(sin/consine)-1/(sine/consine)]/[sine/cosien)+1/(sine/consine)}

Answer
if you mean cosine and not consine

[((sin(x)/cos(x)) - 1)/(sin(x)/cos(x))] / [((sin(x)/cos(x)) + 1)/(sin(x)/cos(x))]

[((sin(x) - cos(x))/cos(x))/(sin(x)/cos(x))] / [((sin(x) + cos(x))/cos(x))/(sin(x)/cos(x))]

working this out, you get

((sin(x) - cos(x))/sin(x)) / ((sin(x) + cos(x))/sin(x)))

working that out, you get

(sin(x) - cos(x))/(sin(x) + cos(x))

((sin(x) - cos(x))*(sin(x) - cos(x))/(sin(x)^2 - cos(x)^2)

(sin(x)^2 - 2sin(x)cos(x) + cos(x)^2)/(-cos(x)^2 + sin(x)^2)

(sin(x)^2 + cos(x)^2 - sin(2x))/(-(cos(x)^2 - sin(x)^2))

(1 - sin(2x))/(-cos(2x))

(-1/cos(2x)) + tan(2x)

-sec(2x) + tan(2x)

[((sin(x)/cos(x)) - 1)/(sin(x)/cos(x))] / [((sin(x)/cos(x)) + 1)/(sin(x)/cos(x))] = tan(2x) - sec(2x)