john1123
john1123 john1123
  • 13-10-2020
  • Mathematics
contestada

6. The value of (tan 1° tan2º tan 3º ... tan 89°) is​

Respuesta :

jimrgrant1 jimrgrant1
  • 13-10-2020

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

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