we have the expression
[tex]\frac{cos(sin^{-1}(\frac{1}{2}))}{tan(cos^{-1}(-\frac{1}{2}))}[/tex]
step 1
Find out the value of sin^-1 (1/2) and cos^-1(-1/2)
[tex]\begin{gathered} sin^{-1}(\frac{1}{2})=30^o \\ cos^{-1}(-\frac{1}{2})=120^0 \end{gathered}[/tex]
substitute in the original expression
[tex]\frac{cos(30^o)}{tan(120^o)}=-\frac{1}{2}[/tex]
Therefore
The answer is -1/2
