Question

Nilai tan 105 . .?
jelaskan . . .

Answer 1

Rumus yang digunakan adalah

                           Tan α + Tan β
Tan (α + β) = --------------------------
                       1 - [Tan α][Tan β]


⇔ Tan 105° = Tan (45° + 60°)

                           Tan 45° + Tan 60°
⇔                = ------------------------------
                       1 - [Tan 45°][Tan 60°]

                          1 + √3
⇔                = --------------
                       1 - [1][√3]

                         1 + √3
⇔                 = -----------
                         1 - √3

Dikali akar sekawan

                         1 + √3     1 + √3
⇔                 = ---------- x ----------
                         1 - √3      1 + √3

                          1 + 2√3 + 3
⇔                 = ------------------
                               1 - 3

                           4 + 2√3
⇔                 = ---------------
                              - 2

⇔                 = - 2 - √3