Diketahui cos A=2/3, cos B=3/5, dimana A dan B sudut lancip. Nilai dari cos (A+B) adalah?

jawab

cos A = 2/3 = x/r
y² = r² - x² = 9 - 4 = 5
y = √5
sin A = y/r = 1/3 √5

cos B = 3/5 =x/r
y²  = r²- x² = 25 - 9 = 16
y = 4
sin B = y/r = 4/5

cos (A+B) = cos A cos B - sin A sin B
= 2/3 .  3/5  - 1/3 √5 . 4/5
= 2/5  - 4/15 √5
= 2/15 ( 3 - 2√5)

TriGonoMetRi

A dan B ---> lancip
sin dan cos ---> (+)

cos A = 2/3
sin A = √(1 - cos² A) = 1/3 √5

cos B = 3/5
sin B = √(1 - cos² B) = 4/5

••
cos (A + B)
= cos A cos B - sin A sin B
= 2/3 . 3/5 - 1/3 √5 . 4/5
= 2/5 - 4/15 √5
= (1/15)(6 - 4√5) ✔