Question

Can anyone evaluate `tan ((5pi)/6) - sin ((7pi)/4) + cot((4pi)/3)` ?

Answer 1

`tan ((5pi)/6) - sin ((7pi)/4) + cot((4pi)/3)`

`=tan (pi-pi/6) - sin (2pi-pi/4) + cot(pi+pi/3)`

`=-tan (pi/6) - (-sin (pi/4)) - cot(pi/3)`

`=-1/sqrt3+1/sqrt2 -1/sqrt3`

`=-2/sqrt3+1/sqrt2`

`=1/(sqrt6)(sqrt3-2sqrt2)`