diketahui sin a = 1/2 sin (a+b) = 2/3 dan sin (a-b) = 3/5 hitunglah nilai tan b

★ Trigomometri ★

sin (a+b) = 2/3
sin a cos b + sin b cos a = 2/3

sin (a-b) = 3/5
sin a cos b - sin b cos a = 3/5

sin a cos b + sin b cos a = 2/3
sin a cos b - sin b cos a = 3/5
———————————————— +
2 sin a cos b =10+9 /15
2 sin a cos b = 18/15
sin a cos b = 6/2*5 = 3/5
cos b = 3/5/1/2 = 3/10

depan b = √10²-3² = √91
sin b = √91/10

maka
tan b
= √91/10/3/10
= √91 / 3