Question

Find the exact value of the expression. Do not use a calculator. StartStartFraction tangent StartFraction pi Over 3 EndFraction OverOver 2 EndEndFraction plus StartStartFraction 1 OverOver cosecant StartFraction pi Over 3 EndFraction EndEndFraction

tangent pi/3 over 2 plus 1 over CSC pi/3

Answer 1

√3

Explanation:

`(1)/(2)\tan{(\pi)/(3)}+\frac{1}{\csc{(\pi)/(3)}}=(1)/(2)\tan{(\pi)/(3)}+\sin{(\pi)/(3)}\\\\=(1)/(2)√(3)+(√(3))/(2)=\boxed{√(3)}`