Diketahui alfa +beta =pi/2,sin alfa cos beta =2/3 dan sin (alfa-beta)=3a.Hitunglah nilai a
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A + B = 90° ( 1 phi = 180°)
sin (A + B) = sin.90°
sin A.cos B + cos A.sin B = 1
2/3 + cos A.sin B = 1 (sin A.cos B = 2/3 didapat dari soal) –
cos A.sin B = 1 – 2/3 = 1/3
sin (A – B) = sin A.cos B – cos A.sin B
3a = 2/3 – 1/3
3a = 1/3
a = (1/3) /3
a = 1/9