Question

if tan15°=X, then
prove that, x² - 2√3 -1 = 0

please...​

Answer 1

Answer:

x² + 2√3 x - 1 = 0

Step-by-step explanation:

Given tan15° = x

 from the properties of trigonometric ratios :

tan30° = 1 / 3

tan( 2A ) = 2tanA / ( 1 - tan²A )

   ⇒ tan( 30° ) = 1 / √3

   ⇒ tan( 2*15° ) = 1 / √3

⇒ 2tan15° / ( 1 - tan²15° ) = 1 / √3

     tan15° = x as given

⇒ 2x / ( 1 - x² ) = 1 / √3

⇒ 2x * √3 = 1( 1 - x² )

⇒ 2√3 x = 1 - x²

⇒ x² + 2√3 x - 1 = 0

   Proved.