Question

Diketahui sin A = 3/5 dan cos b = 5/13. A dan b merupakan sudut lancip. Tentukan tan (a+b) dan tan (a-b).

Answer 1

SinA = 3/5 SinB = 12/13
CosA = 4/5. CosB = 5/13
TanA = 3/4. TanB = 12/5
tan(a+b) = (tan(a)+tan(b))/(1-tan(a).tan(b)) ==> identitas trigonometri
maka
tan(a+b)
= ( 3/4 + 12/5)/(1-(3/4.12/5))
= ( 15/20 + 48/20)/(1-(36/20))
= (63/20)/(16/20)
= 63/16
tan(a-b)
= ( 3/4 - 12/5)/(1+(3/4.12/5))
= ( 15/20 - 48/20)/(1+(36/20))
= (- 33/20)/(56/20)
= -33/56