Jika cot 0 =7/8 hitung nilai dari (1+sin 0).(1-sin 0)/(1+cos 0).(1-cos 0)

Penyelesaian :
Untuk setiap sudut A tertentu
berlaku :
1. tan A = sin A/cos A
2. cotan A = cos A/sin A
3. sec A = 1/cos A
4. cosec A = 1/sin A
5. sin² A + cos² A = 1
6. tan² A + 1 = sec² A
7. 1 + cotan² A = cosec² A
8. sin 2A = 2sin A cos A
9. cos 2A = cos² A - sin² A

Jika cotan 0 = 7/8, maka
tan 0= 8/7

a . (1 + sin 0) . (1 - sin 0)/(1 + cos 0) . (1 - cos 0)
= [1 + sin 0 - sin 0 - sin² 0]/
[1 + cos 0 - cos 0 - cos² 0]
= (1 - sin² 0)/(1 - cos² 0)
= cos² 0/sin² 0
= cotan² 0
= (7/8)²
= 49/64

b. 1 - (tan 0)²/1 + (tan 0)²
= 1 - (8/7)²/1 + (8/7)²
= (1 - 64/49)/(1 + 64/49)
= (49 - 64)/49/(49 + 64)/49
= -15/113