Evaluate tan⁡   1∘×tan⁡28∘×tan⁡35∘×tan⁡62∘×tan⁡89∘×tan⁡55∘tan   1 ∘ ×tan28 ∘ ×tan35 ∘ ×tan62 ∘ ×tan89 ∘ ×tan55 ∘

The given expression is tan(1°) * tan(28°) * tan(35°) * tan(62°) * tan(89°) * tan(55°).

We know that tan(90 - A) = cot(A), which is also equal to 1/tan(A).

So, we can rewrite the expression as follows:

tan(1°) * tan(28°) * tan(35°) * tan(62°) * tan(89°) * tan(55°) = tan(1°) * tan(28°) * tan(35°) * tan(28°) * tan(1°) * tan(35°) = tan(1°)^2 * tan(28°)^2 * tan(35°)^2.

We also know that tan(A) * tan(45 - A) * tan(45 + A) = 1.

So, we can rewrite the expression as follows:

tan(1°)^2 * tan(28°)^2 * tan(35°)^2 = 1^2 = 1.

So, the value of the given expression is 1.