Question

tan(A+B)=(tanA+tanB)/(1-tanA+tanB) and tan15°, prove tan30°=1/√(3)

Answer 1

Hi ,

Tan 15°

= Tan( 45 - 30 )

= ( Tan45 - tan 30 ) / ( 1 - tan45tan30 )

= ( 1 - 1/√3 ) / ( 1 + 1/√3 )

= ( √3 - 1 ) / ( √3 + 1 )

= ( √3 - 1 ) ² / [ (√3 + 1 ) ( √3 - 1 )]

= [ (√3 )² - 2√3 + 1 ] / [ ( √3 )² - 1² ]

= ( 3 - 2√3 + 1 ) / ( 3 - 1 )

= ( 4 - 2√3 ) / 2

= 2 ( 2 - √3 ) / 2

= 2 - √3

I hope this helps you.

:)