[cos(15°)-sin(15°)]/[cos(15°)+sin(15°)]
=[cos(15°)-sin(15°)]²/[cos(15°)-sin(15°)][cos(15°)+sin(15°)]
=[cos²(15°)+sin²(15°)-2sin(15°)cos(15°)]/[cos²(15°)-sin²(15°)]
=[1-sin(30°)]/cos(30°)
=(1/2)/(√3/2)
=√3/3
[cos(15°)-sin(15°)]/[cos(15°)+sin(15°)]
=[cos(15°)-sin(15°)]²/[cos(15°)-sin(15°)][cos(15°)+sin(15°)]
=[cos²(15°)+sin²(15°)-2sin(15°)cos(15°)]/[cos²(15°)-sin²(15°)]
=[1-sin(30°)]/cos(30°)
=(1/2)/(√3/2)
=√3/3