Question

Evaluate LaTeX: \tan(45^{\circ})\cos(30^{\circ}).

Answer 1

To evaluate the expression \(\tan(45^{\circ})\cos(30^{\circ})\), we need to determine the values of \(\tan(45^{\circ})\) and \(\cos(30^{\circ})\).

1. **Calculate \(\tan(45^{\circ})\)**:
\[
\tan(45^{\circ}) = 1
\]

2. **Calculate \(\cos(30^{\circ})\)**:
\[
\cos(30^{\circ}) = \frac{\sqrt{3}}{2}
\]

Now, substituting these values into the original expression:
\[
\tan(45^{\circ})\cos(30^{\circ}) = 1 \cdot \frac{\sqrt{3}}{2}
\]

Thus, the final result is:
\[
\tan(45^{\circ})\cos(30^{\circ}) = \frac{\sqrt{3}}{2}
\]

Therefore, the evaluated expression is:
\[
\boxed{\frac{\sqrt{3}}{2}}
\]