Diketahui cos A.cos B =3/13 dan cos (A+B)=63/65. A dan B sudut lancip hitung cos (A-B)

Jawab:

Penjelasan dengan langkah-langkah:

cos (A+B) = 63/65

cos A cos B – sin A sin B = 63/65

3/13 – sin A sin B = 63/65

sin A sin B = 3/13  - 63/65 = 45/65 – 63/65 =- 18/65

cos (A-B) = cos A cos B + sin A sin B

= 3/13 +(-18/65)

= 45/65 – 18/65

=27/65

Cos(A+B)=CosA.CosB-SinA.SinB

63/65=3/13-SinA.SinB

63/65-3/13=-SinASinB

(63-15)/65=-SinA.SInB

48/65=-SinA.SinB

SinA.SinB=-48/65

Cos(A-B)=CosA.CosB+SinA.SinB

Cos(A-B)=3/13+(-48/65)

Cos(A-B)=(15-48)/65

Cos(A-B)=-33/65