Answer:
1
Step-by-step explanation:
Using the trigonometric identities
tan(90 - x) = cotx , cotx = [tex]\frac{1}{tanx}[/tex]
Given
tan1tan2tan3....................... tan87tan88tan89
= tan1tan2tan3............... tan(90-3)tan(90-2)(tan90 - 1)
= tan1tan2tan3.............. cot3cot2cot1
= tan1cot1tan2cot2tan3cot3 ........................
= 1 × 1 × 1 ×....................... × 1
= 1
