Find the exact value of the following expression without using a calculator.Check your answer with a calculator. (sin(frac (5pi )/(6)))(cos((5pi )/(6))) (sin(frac (5pi )/(6)))(cos((5pi )/(6)))=square (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression )

To find the exact value of the expression \(\frac{\sin\left(\frac{5\pi}{6}\right)}{\cos\left(\frac{5\pi}{6}\right)}\), we can use the trigonometric identity for the tangent function: So, we have: Now, let's find the value of \(\tan\left(\frac{5\pi}{6}\right)\).The angle is in the second quadrant, where the tangent function is negative. We can use the reference angle to find the value of \(\tan\left(\frac{5\pi}{6}\right)\).We know that: Since is in the second quadrant, where the tangent function is negative, we have: :\[\tan\left(\frac{5\pi}{6}\right) = -\frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = -\frac{\sqrt{3}}{3}\]Therefore, the exact value of the expression \(\frac{\sin\left(\frac{5\pi}{6}\right)}{\cos\left(\frac{5\pi}{6}\right)}\) is: