Question

use the sum or difference identify to find the exact vlue of tan 105 degree.my ans.sqrt plus (3) plus 1 . wrong so can you correct it for me please thank you .

Answer 1

105 = 45 +60

tan 45 = 1
tan 60 = sqrt 3
tan(a+b) = (tan a+tan b)/(1-tan a tanb)
=(1+sqrt 3)/(1-sqrt 3)
= (1+sqrt3)(1+sqrt 3)/[(1-sqrt 3)(1+sqrt 3)]
= (4+2sqrt3)/(1-3)
= -(2 + sqrt 3)