Question

How do you solve the trigonometric inequality `-1<=tan(2pi/3-x)<=sqrt(3)` ?

`-1<=tan(2pi/3-x)<=sqrt(3)`

Answer 1

`-1<=tan((2pi)/3-x)<=sqrt3`

`=>tan(-pi/4)<=tan((2pi)/3-x)<=tan(pi/3)`

`=>-pi/4<=(2pi)/3-x<=pi/3`

`=>pi/4>=-(2pi)/3+x>=-pi/3`

`=>(2pi)/3+pi/4>=(2pi)/3-(2pi)/3+x>=(2pi)/3-pi/3`

`=>(11pi)/12>=x>=pi/3`

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