sir
   if sin (A-B)=1/2 & cos (A-B)=1/2 & find A & B

Asked by seeni2005 | 19th Jul, 2016, 06:46: PM

Expert Answer:

begin mathsize 16px style sin left parenthesis straight A minus space straight B right parenthesis equals 1 half
rightwards double arrow sin left parenthesis straight A space minus space straight B right parenthesis equals sin 30 degree
rightwards double arrow straight A space minus space straight B space equals space 30 degree space space space space... left parenthesis 1 right parenthesis
Also comma space cos left parenthesis straight A space plus space straight B right parenthesis equals 1 half
rightwards double arrow cos left parenthesis straight A space plus space straight B right parenthesis equals cos 60 degree
rightwards double arrow straight A space plus space straight B space equals space 60 degree space... left parenthesis 2 right parenthesis
Adding space equations space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis comma space we space get
2 straight A equals space 90 degree rightwards double arrow straight A space equals space 45 degree
Substitute space in space left parenthesis 2 right parenthesis comma space we space get space
straight A space plus space straight B space equals space 60 degree space rightwards double arrow space straight B space equals space 60 degree space minus space 45 degree space rightwards double arrow straight B space equals space 15 degree
Hence comma space straight A space equals space 45 degree space and space straight B space equals space 15 degree. end style

Answered by Rebecca Fernandes | 19th Jul, 2016, 09:30: PM