Question

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

Answer 1

1

Explanation:

Using the trigonometric identities

tan(90 - x) = cotx , cotx =
`(1)/(tanx)`

Given

tan1tan2tan3....................... tan87tan88tan89

= tan1tan2tan3............... tan(90-3)tan(90-2)(tan90 - 1)

= tan1tan2tan3.............. cot3cot2cot1

= tan1cot1tan2cot2tan3cot3 ........................

= 1 × 1 × 1 ×....................... × 1

= 1