Question

find the value of

tan 15°​

Answer 1

Answer :

Step by step explanation :

sin 15° = ( root 3 - 1 ) / 2 root 2

cos 15° = ( root 3 + 1 ) / 2 root 2

tan 15° = sin 15° / cos 15°

= [ ( root 3 - 1 ) / 2 root 2 ] ÷ [ ( root 3 + 1 ) / 2 root 2 ]

= ( root 3 - 1 ) / ( root 3 + 1 )

Answer 2

tan15

= >tan(45 - 30)

= >$\dfrac{ \tan45 - \tan30 }{1 + \tan45 \tan30 }$

= >$\dfrac{1 - \dfrac{1}{ \sqrt{3} } }{1 + 1. \dfrac{1}{ \sqrt{3} } }$

= >$\boxed{\red{ \dfrac{ \sqrt{3} - 1 }{ \sqrt{3} + 1 }}}$