find the exact value of the expression tan135degrees60degree

find the exact value of the expression
tan(135degrees-60degrees)

answer 2+root3

I can\'t figure out how to do this.

Solution

tan ( 135 - 60 )

applying tan ( a- b ) formula

tan (a - b) = ( tan a - tan b ) / ( 1 + tan a tan b )

= ( tan 135 - tan 60 ) / ( 1 + tan 135 * tan 60 )

tan 135 = -1

tan 60 = sqrt 3

plugging the values we get

( -1 - sqrt 3 ) / ( 1 - sqrt 3 )

( -1 - sqrt 3 ) ( 1 + sqrt 3 )/ ( 1- sqrt 3 ) ( 1+ sqrt 3 )

(-1 - sqrt 3 - sqrt 3 - 3) / (1 - 3 )

( -4 - 2 sqrt 3 ) / ( -2 )

( 2 + sqrt 3 )