Tolong bantu jawab! Carilah nilai sin ( alfa+beta), cos (alfa+beta), dan Tan (alfa-beta) jika di ketahui: sin alfa=2/3, cos beta=3/4, alfa kuadran 2 dan beta ku

jawab

A dikuadran II
B dikuadran IV

sin A = 2/3 
cos A = - 1/3 √5
tan A = -2/√5

cosB = 3/4
sin B = - 1/4 √7
tan B = -1/3 √3

sin (A+B) = sin A cos B + cos A sin B
= (2/3. 3/4) + (- 1/3 √5 . -1/4 √7)
= 1/2 + 1/12 √35

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

tan (A-B) = (tan A - tan B)/ (1  + tan A tan B)
= (- 2/√5 + 1/3 √3) / ( 1 + (-2/√5. -1/3 √3)
= (-2 √5  + 1/3 √3) / ( 1 + 2/3 √15)