diketahui cosec A + cot A=3 hitunglah cosec A-cot A please bantuin...

Kategori Soal : Matematika - Trigonometri
Kelas : X (1 SMA)
Pembahasan :
Diketahui 
tan A = sin A/cos A
cotan A = cos A/sin A
sec A = 1/cos A
cosec A = 1/sin A

cosec A + cotan A = 3
⇔ (1/sin A) + (cos A/sin A) = 3
⇔ (1 + cos A)/sin A = 3
⇔ 1 + cos A = 3 sin A
⇔ sin A = (1 + cos A)/3

cosec A - cotan A
= (1/sin A) - (cos A/sin A)
= (1 - cos A)/sin A
= (1 - cos A)/[(1 + cos A)/3]
= [3 . (1 - cos A)]/(1 + cos A)

Semangat!