Pertanyaan

Selesaikanlah persamaan berikut untuk x ∈ R . tan 2 x ∘ = − tan x ∘

Selesaikanlah persamaan berikut untuk $x \in R$ .

$tan 2 x^{\circ} = - tan x^{\circ}$

N. Puspita

Master Teacher

Jawaban terverifikasi

Pembahasan

Dengan menggunakan rumus trigonometri, diperoleh: Sehingga, atau Dengan demikian,

Dengan menggunakan rumus trigonometri, diperoleh:

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan space 2 x degree end cell equals cell negative tan space x degree end cell row cell tan space 2 x degree plus tan space x degree end cell equals 0 row cell fraction numerator 2 tan space x over denominator 1 minus tan squared x end fraction plus tan space x end cell equals 0 row cell fraction numerator 2 tan space x over denominator 1 minus tan squared x end fraction plus fraction numerator tan space x open parentheses 1 minus tan squared x close parentheses over denominator 1 minus tan squared x end fraction end cell equals 0 row cell 2 tan space x plus tan space x open parentheses 1 minus tan squared x close parentheses end cell equals 0 row cell 2 space tan space x plus tan space x minus tan cubed x space end cell equals cell space 0 end cell row cell 3 tan space x minus tan cubed x space end cell equals cell space 0 end cell row cell tan space x left parenthesis 3 minus tan squared x right parenthesis end cell equals 0 row cell tan space x end cell equals cell 0 space atau end cell row cell 3 minus tan squared x end cell equals 0 row cell tan space x end cell equals cell plus-or-minus square root of 3 end cell row blank blank blank end table$

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space x end cell equals 0 row cell tan space x end cell equals cell tan space 0 degree end cell row x equals cell 0 degree plus n times 180 degree end cell end table

atau

Dengan demikian,

x equals open curly brackets table attributes columnalign left end attributes row cell stack 60 degree plus n times 180 degree with 0 degree plus n times 180 degree on top end cell row cell 120 degree plus n times 180 degree end cell end table close space dimana space n element of straight natural numbers