Question

What is the value of tan 1^∘ . tan 2^∘ . tan 3^∘ . ldots . tan 89^∘ ?

a) 0
b) Undefined
c) 1
d) 2

Answer 1

The value of tan 1°. tan 2°. tan 3° ... tan 89° is 1.

Step-by-step explanation:

The question asks for the value of the product of the tangent functions of all the integer degrees from 1 to 89. This is a property of the tangent function that can be used to solve the problem:

Tan(90° - θ) = Cot(θ), which means tan(90° - θ) is also equal to 1/tan(θ).

The value of tan 1°. tan 2°. tan 3° ... tan 89° can be found by noticing a pattern. The tangent function repeats its values every 180°. Since tan 90° is undefined, we can look at the values of tan from 1° to 89° as half of a period. If we pair each angle with its complementary angle (e.g., 1° with 89°, 2° with 88°, etc.), we will get a product of 1 for each pair. Since there are 44 pairs, the overall product will be 1^44, which is equal to 1.