Question

The value of (tan 1° tan 2° ...... tan 89°) is equal to ______.

Answer 1

The value of (tan 1° tan 2° ...... tan 89°) is equal to 1.

Explanation:

tan 1° tan 2° tan 3° ................... tan 89°

= (tan 1° tan 89°) (tan 2° tan 88°) (tan 3° tan 87°) ... (tan 45° tan 45°)

= [tan 1° tan (90° – 1)] [tan 2° tan (90° – 2)] [tan 3° tan (90° – 3)] ............. [tan 45° tan (90° – 45°)]

= (tan 1° cot 1°) (tan 2° cot 2°) (tan 3° cot 3°) ............. [tan 45° cot 45°]

= `(tan 1^circ xx 1/(tan 1^circ)) (tan 2^circ xx 1/(tan 2^circ)) (tan 3^circ xx 1/(tan 3^circ)) ... [tan 45^circ xx 1/(tan 45^circ)]`

= 1 × 1 × 1 ............. 1 × 1

= 1