Question

Hitunglah: tan 195° + tan 105° - tan 60°

Answer 1

Tan 195 + tan 105 - tan 60
tan 195 = tan (135+60)
= (tan 135 + tan 60)/(1 - tan 135.tan 60)
= (-1 + √3) /(1 - (-1)(√3)
=(-1 + √3)/(1 +√3)
= (-1+√3)(1-√3)/ ( 1 - 3)
= (-4 +2√3)/(-2)
= 2-√3

tan105 = tan(60+45)
= (tan 60 + tan 45) / (1 - tan 60. tan45)
= (√3+ 1)/ (1 - √3)
= (4 + 2√3)/ (-2)
= -2 - √3
..
tan 60 = √3
.
tan 195 + tan 105 - tan 60 =
= 2 - √3 - 2 - √3 - √3
= - 3√3