1. Diketahui sin A = 5/13 dan cos B = 3/5 , A dan B di kuadran I Tentukan a. Sin 2A + cos 2 B b. Sin (A + B) c. Tan (A – B)

Semoga membantu ya ^^.......

Sin A = - 5/13
tan A = 5/12

cos B = 3/5
tan B = 4/3

a.

b. sin (A+B)
= sin A cos B + cos A sin B
= 3/5 x (-12/13) + 4/5 x 5/13
= -36/65 + 20/65
= -16/65

c. tan A = sin A/cos A
= (3/5)/(4/5) = 3/4
tan B = sin B/cos B = (5/13)/(-12/13) = -5/12
Maka,
tan (A-B)
= (tan A-tan B) / (1 + tan A tan B)
= (3/4-(-5/12)) / (1 + 3/4 x (-5/12))
= ( (9+5)/12) / (1 - 5/16)
= (14/12) / (11/16)
= 7/6 : 11/16
= 7/6 x 16/11
= 7/3 x 8/11
= 56/33

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