Diketahui segitiga ABC siku-siku di C. Jika sin(A-B)=5a, sinA.sinB=2/5, maka a=....

sinia4/6 dan ABC dari sin ABC

∆ABC siku di C

A + B = 90°

sin (A - B) = 5a
sin (A + B) = 1
---------------------- (+)
2 sin A cos B = 1 + 5a

cos (A + B) = 0
cos A cos B = sin A sin B = 2/5
tan A tan B = 1

2 sin A cos B = 1 + 5a
Kedua ruas (: cos A cos B)
2 . tan A tan B = (1 + 5a)/(2/5)
2 . 1 = (1 + 5a) × 5/2
1 + 5a = 2 × 2/5
5a = 4/5 - 1
5a = -1/5
a = -1/25 ✔