Jika cos p= akar 7/11 dan p sudut lancip maka tentukan nilai cot(360-p)-1 / cosec(180+p)

Materi : Trigonometri

Pembahasan :
Identitas Trigonometri
Sin²p + Cos²p = 1
Sin²p = 1 - Cos²p
Sin²p = 1 - (√7/11)²
Sin²p = 1 - 7/121
Sin²p = 114/121
Sin p = (√114)/11

[Cot (360° - p) - 1]/[Cosec (180° + p)]
= [- Cot p - 1]/[- 1/Sin p]
= [Cot p + 1]/[1/Sin p]
= Sin p . Cot p + Sin p
= Sin p . Cos p / Sin p + Sin p
= Cos p + Sin p
= (√7)/11 + (√114)/11
= (√141 + √7)/11

cos p = √7 /11
sin p = √(1 - cos² p)
sin p = √(1 - (7/121))
sin p = √((121 - 7)/121)
sin p = (1/11)√114

(cot (360° - p) - 1) / (cosec (180° + p))
= (-cot p - 1) / (- cosec p)
= -(cot p + 1)/(-1/sin p)
= sin p (cos p/sin p + 1)
= cos p + sin p
= √11 /11 + √114 /11
= (1/11)(√11 + √114)