find the exact value

Question

express your result as a single, simplified fraction in radical form.

 equation:

 

 tan(11π/6) - cos(5π/6)

Answer 1

looking on the unit circle...

tan(11∏/6)-cos(5∏/6)

(-1/2)/(√3/2)-(-√3/2)

(-1/√3)+(√3/2)

(-√3/3)+(√3/2)

(-2√3/6)+(3√3/6)

√3/6