I try to avoid the half angle formula.
Instead I would multiply by the conjugate on top and bottom.
It works, but you need to break up the fraction into two pieces
and then there's a little partial fraction problem to solve, but it should work.
This has been bugging me for a long time now... Can anyone please help me?
Integrate dx/(sin(x) + cos(x))
I used the identy that t= tan(x/2)
So following the sin and cos substitutaion I have
dx = 2dt/1+t^2
sin(x) = 2t/(1+t^2)
cos(x) = (1-t^2)/(1+t^2)
thus we have
Integral (2dt/(1+t^2))/((2t + 1-t^2)/(1+t^2)
this simplifies to
Integral 2dt/(2t+1-t^2)
then factor down into
Integral -2dt/(t-1)^2 -2
t=sqrt(2)sec(a) +1
Integral -2dt/2(sec(a)^2 -1)
Integral -dt/(tan^2(a))
Am I way off?? there seems to be way to many substitutions or something... I would appreciate it very much!