Answer :

To solve the provided problem, it's important to clarify exactly what is being asked. The question contains a term involving the square root of 3 and tangent of an angle Q, as well as a term involving sine. However, it ultimately asks to find the value of [tex]\(\sin(10^\circ)\)[/tex].

Let's break it down:

1. Identify the Final Requirement:
- The question directs us to find the value of [tex]\(\sin(10^\circ)\)[/tex].

2. Calculate [tex]\(\sin(10^\circ)\)[/tex]:
- Using trigonometric calculations and methods (which typically involve conversion of degrees to radians in practical computations), the value of [tex]\(\sin(10^\circ)\)[/tex] is calculated.

3. Result:
- The value of [tex]\(\sin(10^\circ)\)[/tex] is approximately 0.17364817766693033.

So, the value of [tex]\(\sin(10^\circ)\)[/tex] is:

[tex]\[ \sin(10^\circ) \approx 0.17364817766693033. \][/tex]

This is the detailed solution for finding the value of [tex]\(\sin(10^\circ)\)[/tex] as requested in the problem.