Question

Tg105°-cotg105° = ?
Please help fast!!! Please

Answer 1

Using only the trig ratios of 45 and 60 degrees, we use angle-sum to compute
`\tan 105^\circ=\tan(60^\circ+45^\circ)=(\tan 60^\circ+\tan 45^\circ)/(1-\tan 60^\circ\tan 45^\circ)=(√(3)+1)/(1-√(3))=-2-√(3),` so
`\cot 105^\circ=(1)/(\tan 105^\circ)=-2+√(3)` and
`\tan 105^\circ-\cot105^\circ=\boxed{-2√(3)}.`