Question

if sinA=3/5 and cosB=5/13 ,prove that cos(A-B)=56/65​

Answer 1

Answer:

Step-by-step explanation:

cos(A-B)=56/65

COS(A-B)=COS A ×COS B+SIN A ×SINB

SIN²A+COS²A=1

COSA=√1-SIN²A=4/5

SIMILARLY SIN B=√1-COS²B=12/13

∴COS(A-B)=(4/5)×(5/13 )+(3/5)(12/13)=56/65