double angles: prove 1 - tanx/1 + tanx = cos2x / sin2x + 1

[ratz4]

i need a hand proving this

1 - tanx/1 + tanx = cos2x / sin2x + 1

i got the L.S. to this point
cosx - sinx / sinx + cosx

now i am having trouble doing the R.S. though i am just not seeing something

 

[Deleted member 4993]

Re: double angle question

i need a hand proving this

1 - tanx/1 + tanx = cos2x / sin2x + 1

i got the L.S. to this point
cosx - sinx / sinx + cosx

now i am having trouble doing the R.S. though i am just not seeing something

First you need to use parentheses to group your operation.

You got

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

multiply the numerator and the denominator by [cos(x) + sin(x)] - expand and apply:

cos[sup:l7gr27o1]2[/sup:l7gr27o1](x) - sin[sup:l7gr27o1]2[/sup:l7gr27o1](x) = cos(2x)

and

2sin(x)cos(x) = sin(2x)