Sin(z+y) = cos(z+y), show that tan(z) = (1-tan(y))/(1+tan(y))

[thatstheguy9]

[MATH] If sin(z+y) = cos(z+y) [/MATH]
[MATH] show: tan(z) = \frac{1-tan(y)}{1+tan(y)} [/MATH]

I have no idea how to start, any hints would be helpful!

 

[Romsek]

I would start by noting the angles at which the condition holds.

Then you can express z in terms of y and expand out tan(z)

Things simplify and then by dividing everything by cos(y) your desired expression will pop out.