diketahui sin A = 12\13 dan tan B = 8/15 ,dengan A dan B sudut lancip. tentukan nilai dari cos (A + B)

jawab

A dan B lancip

sin A = 12/13 = y/r → x,y,r = 5,12,13 (triple)
cos A = x/r = 5/13

tan B = 8/15 = y/x →x,y,r = 15,8, 17 (triple)
sin B = y/r = 8/17
cos B = x/r = 15/17

cos (A + B) = cos A cos B - sin A sin B
= 5/13 (15/17) - 12/13 (8/17)
=  75/221 - 96/221
= 21/221

TriGonoMetRi

sin A = 12/13
cos A = √(1 - sin² A) = 5/13

tan B = 8/15
sin B = 8/√(8² + 15²) = 8/17
cos B = 15/√(8² + 15²) = 15/17

cos (A + B)
= cos A cos B - sin A sin B
= 5/13 . 15/17 - 12/13 . 8/17
= (75 - 96)/(13 . 17)
= -21/221