Question

Diketahui nilai cos (alfa+beta)=2/3 dan cos alfa cos beta=1/2. Jika alfa+beta lancip maka nilai tan (alfa+beta) adalah...
A. 1/4 akar 2
B. 1/2
C. 2/3 akar 2
D. 2
E. 2 akar 2

Answer 1

Sin² x + cos² x = 1

cos (a + b) = 2/3
sin (a + b) = √(1 - cos² (a + b))
sin (a + b) = √(1 - (4/9))
sin (a + b) = 1/3 √5

tan (a + b)
= sin (a + b) / cos (a + b)
= 1/3 √5 / 2/3
= 1/2 √5