Find the Value of tan 1° tan 2° tan 3° … tan 89°

We will use different tan identities to find out the value of the expression.

Answer: The value of tan 1° tan 2° tan 3° … tan 89° = 1

Let us go to the step-by-step solution below.

Explanation:

Let, N = tan 1° tan 2° tan 3° … tan 89°

N = [tan 1° tan 2° … tan 44°] tan 45° [tan (90° – 44°).tan (90° – 43°)… tan (90° – 1°)]

N = [tan 1° tan 2° … tan 44°].tan 45°.[cot 44°.cot 43°... cot 1°]

We know, tan Ø × cot Ø = 1 and tan 45° = 1

Therefore, simplifying N further, we get N = 1 

Thus, the value of tan 1° tan 2° tan 3° … tan 89° = 1