find cos(a+b) if sina=1 and cosb=1

Answer 1

general formula is

cos(A+B) = cosAcosB - sinASinB

If sinA= cosB=1

then cos(A+B) = cosA-sinB

also if sinA=1, then cosA =0 and A=pi/2

if cosB=1, then sinB =0 and B=0

plug those values into

cos(A+B) = cosA - sinB

cos(pi/2 + 0) = 0-0

cos(pi/2) = cos(90 degrees) = 0

A actually = pi/2 + 2npi where n = any integer

and B = 2npi where n= any integer

but A=pi/2 and B=0 is the easiest way to look at the probelm