Perhatikan gambar berikut. Pernyataan yang benar adalah? (No.5)

Jika α = 120° maka

1.) 2(sin α + cos α) = (1 + √3)

• sin 210° = sin(180° + 30°)
= – sin 30° = – ½
• cos 210° = cos(180° + 30°)
= – cos 30° = – ½√3

2(-½ – ½√3) = -1 – √3 (salah)

2.) tan α + cot α = ⁴/₃√3

• tan 210° = tan(180° + 30°)
= tan 30° = ⅓√3
• cot 210° = 1/(tan 210°)
= √3

⅓√3 + √3 = ⅓√3 + ³/₃√3 = ⁴/₃√3 (benar)

4.) cosec α + sec α = -⅔(3 + √3)

• cosec 210°= 1/(sin 210°)
= -2
• sec 210° = 1/(cos 210°)
= -⅔√3

-2 + ⅔√3 = -⅔(3 + √3)
(benar)

Jawaban : C