Question

The value of tan 1° tan 2° tan 3° ...... tan 89° is
(a)
(b) −1
(c)0
(d)None of these

Answer 1

SOLUTION :  

The correct option is  (a)  : 1

Given : tan 1° tan 2° tan 3° ……….  tan 89°

tan 1° tan 2° tan 3° ……….  tan 89°

= tan (90° - 89°) tan (90° - 88°) …….. tan 87° tan 88°tan 89°

= cot 89° cot 88°……... tan 87° tan 88°tan 89°

[tan θ = cot (90 - θ) ]

= (cot 89° tan 89° ) (cot 88° tan 88°)(cot 87° tan 87°

= 1 × 1 × 1

[tan θ × cot θ = 1]

tan 1° tan 2° tan 3° ……….  tan 89° = 1  

Hence, the value of tan 1° tan 2° tan 3° ……….  tan 89° is 1.

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

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