To find the value of tan 1° tan 2° tan 3° tan 89°, we can use some properties of the tangent function. One crucial property to consider is that
tan(90° – x) = cot x,
which means that tan 89° = cot 1°. Since cotangent is the reciprocal of tangent, we have:
tan 89° = 1 / tan 1°.
Now, substituting this back into our original expression:
tan 1° tan 2° tan 3° tan 89° = tan 1° tan 2° tan 3° (1 / tan 1°)
Here, the tan 1° terms cancel each other out:
tan 2° tan 3°.
Unfortunately, there isn’t a straightforward exact value for tan 2° tan 3°, but it can be computed using a calculator. However, we can recognize that:
tan 90° = undefined, as tangent approaches infinity at that angle.
Thus, the resultant value is:
tan(1°) * tan(2°) * tan(3°) * tan(89°) = tan(2°) * tan(3°).